Adams, D.R. 1988. A sharp inequality of J. Moser for higher order derivatives. Ann. Math. (2), 128(2), 385–398.CrossRefGoogle Scholar

Ahlfors, L.V. 1954. On quasiconformal mappings. J. Anal. Math., 3, 1–58; correction, 207–208.Google Scholar

Ahlfors, L.V. 1966. Lectures on Quasiconformal Mappings. Manuscript prepared with the assistance of Clifford J. Earle, Jr. Van Nostrand Mathematical Studies, No. 10. Toronto, Ontario–New York–London: D. Van Nostrand Co., Inc.Google Scholar

Ahlfors, L.V. 1973. Conformal Invariants: Topics in Geometric Function Theory. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill Book Co.Google Scholar

Ahlfors, L.V. 1978. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. Third edn. International Series in Pure and Applied Mathematics. New York: McGraw-Hill Book Co.Google Scholar

Ahlfors, L.V. 1981. Möbius Transformations in Several Dimensions. Ordway Professorship Lectures in Mathematics. Minneapolis: University of Minnesota School of Mathematics.Google Scholar

Almgren, Jr., F.J., and Lieb, E.H. 1989. Symmetric decreasing rearrangement is sometimes continuous. J. Amer. Math. Soc., 2(4), 683–773.Google Scholar

Alvino, A., Trombetti, G., and Lions, P.-L. 1990. Comparison results for elliptic and parabolic equations via Schwarz symmetrization. Ann. Inst. H. Poincaré Anal. Non Linéaire, 7(2), 37–65.Google Scholar

Alvino, A., Lions, P.-L., and Trombetti, G. 1991. Comparison results for elliptic and parabolic equations via symmetrization: a new approach. Differ. Integr. Equ., 4(1), 25–50.Google Scholar

Alvino, A., Trombetti, G., and Matarasso, S. 2002. Elliptic boundary value problems: comparison results via symmetrization. Ricerche Mat., 51(2), 341–355.Google Scholar

Anderson, G.D., Vamanamurthy, M.K., and Vuorinen, M.K. 1997. Conformal Invariants, Inequalities, and Quasiconformal Maps. Canadian Mathematical Society Series of Monographs and Advanced Texts. New York: John Wiley & Sons Inc.Google Scholar

Anderson, J.M., and Baernstein, II, A. 1978. The size of the set on which a meromorphic function is large. Proc. London Math. Soc. (3), 36(3), 518–539.Google Scholar

Andrews, G.E., Askey, R., and Roy, R. 1999. Special Functions. Encyclopedia of Mathematics and Its Applications, vol. 71. Cambridge: Cambridge University Press.Google Scholar

Ashbaugh, M.S., and Benguria, R.D. 1992. A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions. Ann. Math. (2), 135(3), 601–628.Google Scholar

Ashbaugh, M.S., and Benguria, R.D. 1994. Isoperimetric inequalities for eigenvalue ratios. Pages 1–36 of: Partial Differential Equations of Elliptic Type (Cortona, 1992). Symposia Mathematica, XXXV. Cambridge: Cambridge University Press.Google Scholar

Ashbaugh, M.S., and Benguria, R.D. 1995. On Rayleigh’s conjecture for the clamped plate and its generalization to three dimensions. Duke Math. J., 78(1), 1–17.Google Scholar

Ashbaugh, M.S., Benguria, R.D., and Laugesen, R.S. 1997. Inequalities for the first eigenvalues of the clamped plate and buckling problems. Pages 95–110 of: General Inequalities, 7 (Oberwolfach, 1995). International Series of Numerical Mathematics, vol. 123. Basel: Birkhäuser.Google Scholar

Astala, K., Iwaniec, T., and Martin, G. 2009. Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton Mathematical Series, vol. 48. Princeton, NJ: Princeton University Press.Google Scholar

Atkinson, K., and Han, W. 2012. Spherical Harmonics and Approximations on the Unit Sphere: An Introduction. Lecture Notes in Mathematics, vol. 2044. Heidelberg: Springer.CrossRefGoogle Scholar

Aubin, T. 1976. Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geometry, 11(4), 573–598.Google Scholar

Baernstein, II, A. 1997. Comparison of p-harmonic measures of subsets of the unit circle. Algebra i Analiz, 9(3), 141–149.Google Scholar

Baernstein, II, A. 1973. Proof of Edrei’s spread conjecture. Proc. London Math. Soc. (3), 26, 418–434.Google Scholar

Baernstein, II, A. 1974. Integral means, univalent functions and circular symmetrization. Acta Math., 133, 139–169.Google Scholar

Baernstein, II, A. 1977. Regularity theorems associated with the spread relation. J. Anal. Math., 31, 76–111.Google Scholar

Baernstein, II, A. 1978. Some sharp inequalities for conjugate functions. Indiana Univ. Math. J., 27(5), 833–852.Google Scholar

Baernstein, II, A. 1980. How the ∗-function solves extremal problems. Pages 639–644 of: Proceedings of the International Congress of Mathematicians (Helsinki, 1978). Helsinki: Acad. Sci. Fennica.Google Scholar

Baernstein, II, A. 1987a. Dubinin’s symmetrization theorem. Pages 23–30 of: Complex Analysis, I (College Park, Md., 1985–86). Lecture Notes in Mathematics, vol. 1275. Berlin: Springer.Google Scholar

Baernstein, II, A. 1987b. On the harmonic measure of slit domains. Complex Variables Theory Appl., 9(2–3), 131–142.Google Scholar

Baernstein, II, A. 1989a. Convolution and rearrangement on the circle. Complex Variables Theory Appl., 12(1–4), 33–37.Google Scholar

Baernstein, II, A. 1989b. Some topics in symmetrization. Pages 111–123 of: Harmonic Analysis and Partial Differential Equations (El Escorial, 1987). Lecture Notes in Mathematics, vol. 1384. Berlin: Springer.Google Scholar

Baernstein, II, A. 1993. An extremal property of meromorphic functions with n-fold symmetry. Complex Variables Theory Appl., 21(3–4), 137–148.Google Scholar

Baernstein, II, A. 1994. A unified approach to symmetrization. Pages 47–91 of: Partial Differential Equations of Elliptic Type (Cortona, 1992). Sympos. Math., XXXV. Cambridge: Cambridge University Press.Google Scholar

Baernstein, II, A. 2002. The ∗-function in complex analysis. Pages 229–271 of: Handbook of Complex Analysis: Geometric Function Theory, Vol. 1. Amsterdam: North-Holland.Google Scholar

Baernstein, II, A., and Brown, J.E. 1982. Integral means of derivatives of monotone slit mappings. Comment. Math. Helv., 57(2), 331–348.Google Scholar

Baernstein, II, A., and Loss, M. 1997. Some conjectures about L ^p norms of k-plane transforms. Rend. Sem. Mat. Fis. Milano, 67, 9–26 (2000).Google Scholar

Baernstein, II, A., and Manfredi, J.J. 1983. Topics in quasiconformal mapping. Pages 819–862 of: Topics in Modern Harmonic Analysis, Vol. I, II (Turin/Milan, 1982). Rome: Istituto Nazionale di Alta Matematica “Francesco Severi”.Google Scholar

Baernstein, II, A., and Schober, G. 1980. Estimates for inverse coefficients of univalent functions from integral means. Israel J. Math., 36(1), 75–82.Google Scholar

Baernstein, II, A., and Taylor, B.A. 1976. Spherical rearrangements, subharmonic functions, and ∗-functions in n-space. Duke Math. J., 43(2), 245–268.Google Scholar

Baernstein, II, A., Laugesen, R.S., and Pritsker, I.E. 2011. Moment inequalities for equilibrium measures in the plane. Pure Appl. Math. Q., 7(1), 51–86.Google Scholar

Bandle, C. 1980. Isoperimetric Inequalities and Applications. Monographs and Studies in Mathematics, vol. 7. Boston: Pitman (Advanced Publishing Program).Google Scholar

Bañuelos, R., and Carroll, T. 1994. Brownian motion and the fundamental frequency of a drum. Duke Math. J., 75(3), 575–602.Google Scholar

Bañuelos, R., van den Berg, M., and Carroll, T. 2002. Torsional rigidity and expected lifetime of Brownian motion. J. London Math. Soc. (2), 66(2), 499–512.Google Scholar

Barthe, F. 1998. Optimal Young’s inequality and its converse: a simple proof. Geom. Funct. Anal., 8(2), 234–242.Google Scholar

Barthe, F. 2003. Autour de l’inégalité de Brunn-Minkowski. Ann. Fac. Sci. Toulouse Math. (6), 12(2), 127–178.Google Scholar

Beckner, W. 1975. Inequalities in Fourier analysis. Ann. Math. (2), 102(1), 159–182.Google Scholar

Beckner, W. 1991. Moser-Trudinger inequality in higher dimensions. Int. Math. Res. Notices, no. 7, 83–91.Google Scholar

Beckner, W. 1992. Sobolev inequalities, the Poisson semigroup, and analysis on the sphere S ⁿ . Proc. Natl. Acad. Sci. U.S.A., 89(11), 4816–4819.Google Scholar

Beckner, W. 1993. Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Ann. Math. (2), 138(1), 213–242.Google Scholar

Beckner, W. 1995. Geometric inequalities in Fourier anaylsis. Pages 36–68 of: Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, NJ, 1991). Princeton Math. Ser., vol. 42. Princeton, NJ: Princeton University Press.Google Scholar

Bennett, C., and Sharpley, R. 1988. Interpolation of Operators. Pure and Applied Mathematics, vol. 129. Boston: Academic Press Inc.Google Scholar

Bennett, J., Carbery, A., Christ, M., and Tao, T. 2008. The Brascamp–Lieb inequalities: finiteness, structure and extremals. Geom. Funct. Anal., 17(5), 1343–1415.Google Scholar

Bérard, P. 1986. Analysis on Riemannian Manifolds and Geometric Applications: An Introduction. Monografías de Matemática [Mathematical Monographs], vol. 42. Rio de Janeiro: Instituto de Matemática Pura e Aplicada (IMPA).Google Scholar

Betsakos, D. 2004. Symmetrization, symmetric stable processes, and Riesz capacities. Trans. Amer. Math. Soc., 356(2), 735–755.Google Scholar

Bhayo, B.A., and Vuorinen, M. 2011. On Mori’s theorem for quasiconformal maps in the n-space. Trans. Amer. Math. Soc., 363(11), 5703–5719.Google Scholar

Blaschke, W. 1917. Über affine Geometrie XI: Lösung des “Vierpunktproblems” von Sylvester aus der Theorie der geometrischen Wahrscheinlichkeiten. Leipziger Ber., 69, 436–453.Google Scholar

Blaschke, W. 1923. Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. II. Affine Differentialgeometrie. Berlin: Springer-Verlag.CrossRefGoogle Scholar

Bliss, G.A. 1930. An integral inequality. J. London Math. Soc., 5(11), 40–46.Google Scholar

Blumenthal, R.M., and Getoor, R.K. 1968. Markov Processes and Potential Theory. Pure and Applied Mathematics, Vol. 29. New York: Academic Press.Google Scholar

Bobkov, S. 1996. A functional form of the isoperimetric inequality for the Gaussian measure. J. Funct. Anal., 135(1), 39–49.Google Scholar

Bobkov, S.G., and Houdré, C. 1997. Some connections between isoperimetric and Sobolev-type inequalities. Mem. Amer. Math. Soc., 129(616).Google Scholar

Bonnesen, T., and Fenchel, W. 1987. Theory of Convex Bodies. Translated from the German and edited by L. Boron, C. Christenson and B. Smith. Moscow, ID: BCS Associates.Google Scholar

Borell, C. 1975. The Brunn-Minkowski inequality in Gauss space. Invent. Math., 30(2), 207–216.Google Scholar

Borell, C. 1985. Geometric bounds on the Ornstein-Uhlenbeck velocity process. Z. Wahrsch. Verw. Gebiete, 70(1), 1–13.Google Scholar

Brascamp, H.J., Lieb, E.H., and Luttinger, J.M. 1974. A general rearrangement inequality for multiple integrals. J. Funct. Anal., 17, 227–237.Google Scholar

Brascamp, H.J., and Lieb, E.H. 1976. On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Funct. Anal., 22(4), 366–389.Google Scholar

Brenier, Y. 1991. Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math., 44(4), 375–417.Google Scholar

Brock, F., and Solynin, A.Y. 2000. An approach to symmetrization via polarization. Trans. Amer. Math. Soc., 352(4), 1759–1796.Google Scholar

Brothers, J.E., and Ziemer, W.P. 1988. Minimal rearrangements of Sobolev functions. J. Reine Angew. Math., 384, 153–179.Google Scholar

Burago, Y.D., and Zalgaller, V.A. 1988. Geometric Inequalities. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 285. Translated from the Russian by A. B. Sosinskiĭ, Springer Series in Soviet Mathematics. Berlin: Springer-Verlag.Google Scholar

Burchard, A. 1997. Steiner symmetrization is continuous in W ^1,p . Geom. Funct. Anal., 7(5), 823–860.Google Scholar

Burchard, A., and Schmuckenschläger, M. 2001. Comparison theorems for exit times. Geom. Funct. Anal., 11(4), 651–692.Google Scholar

Burchard, A. 1996. Cases of equality in the Riesz rearrangement inequality. Ann. Math. (2), 143(3), 499–527.Google Scholar

Burchard, A., and Ferone, A. 2015. On the extremals of the Pólya-Szegő inequality. Indiana Univ. Math. J., 64(5), 1447–1463.Google Scholar

Burchard, A., and Hajaiej, H. 2006. Rearrangement inequalities for functionals with monotone integrands. J. Funct. Anal., 233(2), 561–582.Google Scholar

Caccioppoli, R. 1953. Misura e integrazione degli insiemi dimensionalmente orientati. Rend. Acc. Naz. Lincei, 12, 3–11.Google Scholar

Carleman, T. 1918. Über ein Minimalproblem der mathematischen Physik. Math. Z., 1(2–3), 208–212.Google Scholar

Carlen, E., and Loss, M. 1992. Competing symmetries, the logarithmic HLS inequality and Onofri’s inequality on S ⁿ . Geom. Funct. Anal., 2(1), 90–104.Google Scholar

Carleson, L., and Chang, S.-Y.A. 1986. On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. (2), 110(2), 113–127.Google Scholar

Cartwright, M.L. 1956. Integral Functions. Cambridge Tracts in Mathematics and Mathematical Physics, No. 44. Cambridge: Cambridge University Press.Google Scholar

Chang, S.-Y.A. 1996. The Moser-Trudinger inequality and applications to some problems in conformal geometry. Pages 65–125 of: Nonlinear Partial Differential Equations in Differential Geometry (Park City, UT, 1992). IAS/Park City Math. Ser., vol. 2. Providence, RI: Amer. Math. Soc.Google Scholar

Chasman, L.M., and Langford, J.J. 2016. The clamped plate in Gauss space. Ann. Mat. Pura Appl. (4), 195(6), 1977–2005.Google Scholar

Chavel, I. 1993. Riemannian Geometry—A Modern Introduction. Cambridge Tracts in Mathematics, vol. 108. Cambridge: Cambridge University Press.Google Scholar

Chavel, I. 2001. Isoperimetric Inequalities. Cambridge Tracts in Mathematics, vol. 145. Cambridge: Cambridge University Press.Google Scholar

Chiti, G. 1979. Rearrangements of functions and convergence in Orlicz spaces. Applicable Anal., 9(1), 23–27.Google Scholar

Chong, K.M. 1975. Variation reducing properties of decreasing rearrangements. Canad. J. Math., 27, 330–336.Google Scholar

Christ, M. 1984. Estimates for the k-plane transform. Indiana Univ. Math. J., 33(6), 891–910.Google Scholar

Cianchi, A., and Fusco, N. 2006. Minimal rearrangements, strict convexity and critical points. Appl. Anal., 85(1–3), 67–85.Google Scholar

Cordero-Erausquin, D., Nazaret, B., and Villani, C. 2004. A mass-transportation approach to sharp Sobolev and Gagliardo–Nirenberg inequalities. Adv. Math., 182(2), 307–332.Google Scholar

Crandall, M.G., and Tartar, L. 1980. Some relations between nonexpansive and order preserving mappings. Proc. Amer. Math. Soc., 78(3), 385–390.Google Scholar

Crowe, J.A., Zweibel, J.A., and Rosenbloom, P.C. 1986. Rearrangements of functions. J. Funct. Anal., 66(3), 432–438.Google Scholar

Davies, E.B. 1989. Heat Kernels and Spectral Theory. Cambridge Tracts in Mathematics, vol. 92. Cambridge: Cambridge University Press.Google Scholar

Davis, B. 1974. On the weak type (1,1) inequality for conjugate functions. Proc. Amer. Math. Soc., 44, 307–311.Google Scholar

Davis, B. 1976. On Kolmogorov’s inequalities . Trans. Amer. Math. Soc., 222, 179–192.Google Scholar

de Branges, L. 1985. A proof of the Bieberbach conjecture. Acta Math., 154(1–2), 137–152.Google Scholar

De Giorgi, E. 1954. Su una teoria generale della misura (r − 1)-dimensionale in uno spazio ad r dimensioni. Ann. Mat. Pura Appl. (4), 36, 191–213.Google Scholar

De Giorgi, E. 1955. Nuovi teoremi relativi alle misure (r − 1)-dimensionali in uno spazio ad r dimensioni. Ricerche Mat., 4, 95–113.Google Scholar

Dieudonné, J. 1951. Sur les espaces de Köthe. J. Anal. Math., 1, 81–115.Google Scholar

Doob, J.L. 1953. Stochastic Processes. New York: John Wiley & Sons Inc.Google Scholar

Draghici, C. 2005. A general rearrangement inequality. Proc. Amer. Math. Soc., 133(3), 735–743.Google Scholar

Drasin, D. 1976. The inverse problem of the Nevanlinna theory. Acta Math., 138(1–2), 83–151.Google Scholar

Drasin, D. 2015. Albert Baernstein II 1941–2014. Notices Amer. Math. Soc., 62(7), 815–818.Google Scholar

Drasin, D., and Weitsman, A. 1975. Meromorphic functions with large sums of deficiencies. Adv. Math., 15, 93–126.Google Scholar

Dubinin, V.N. 1987. Transformation of condensers in space. Dokl. Akad. Nauk SSSR, 296(1), 18–20.Google Scholar

Dubinin, V.N. 1993. Capacities and geometric transformations of subsets in n-space. Geom. Funct. Anal., 3(4), 342–369.Google Scholar

Dubinin, V.N. 2014. Condenser Capacities and Symmetrization in Geometric Function Theory. Translated from the Russian by N. G. Kruzhilin. Basel: Springer.Google Scholar

Dunford, N., and Schwartz, J.T. 1958. Linear Operators. I. General Theory. With the assistance of W.G. Bade and R.G. Bartle. Pure and Applied Mathematics, Vol. 7. New York: Interscience Publishers, Inc.Google Scholar

Duren, P.L. 1983. Univalent Functions. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259. New York: Springer-Verlag.Google Scholar

Durrett, R. 1984. Brownian Motion and Martingales in Analysis. Wadsworth Mathematics Series. Belmont, CA: Wadsworth International Group.Google Scholar

Edrei, A. 1965. Sums of deficiencies of meromorphic functions. J. Anal. Math., 14, 79–107.Google Scholar

Edrei, A. 1970. A local form of the Phragmén–Lindelöf indicator. Mathematika, 17, 149–172.Google Scholar

Edrei, A. 1973. Solution of the deficiency problem for functions of small lower order. Proc. London Math. Soc. (3), 26, 435–445.Google Scholar

Edrei, A., and Fuchs, W.H.J. 1960. The deficiencies of meromorphic functions of order less than one. Duke Math. J., 27, 233–249.Google Scholar

Ehrhard, A. 1983a. Symétrisation dans l’espace de Gauss. Math. Scand., 53(2), 281–301.Google Scholar

Ehrhard, A. 1983b. Un principe de symétrisation dans les espaces de Gauss. Pages 92– 101 of: Probability in Banach Spaces, IV (Oberwolfach, 1982). Lecture Notes in Math., vol. 990. Berlin: Springer.Google Scholar

Ehrhard, A. 1984. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes. Ann. Sci. École Norm. Sup. (4), 17(2), 317–332.Google Scholar

Epperson, J.B. 1990. A class of monotone decreasing rearrangements. J. Math. Anal. Appl., 150(1), 224–236.Google Scholar

Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. 1954. Tables of Integral Transforms. Vol. II. New York–Toronto–London: McGraw-Hill Book Company, Inc. Based, in part, on notes left by Harry Bateman.Google Scholar

Essén, M., Rossi, J., and Shea, D. 1993. A convolution inequality with applications to function theory. II. J. Anal. Math., 61, 339–366.Google Scholar

Evans, L.C. 1998. Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. Providence, RI: American Mathematical Society.Google Scholar

Evans, L.C., and Gariepy, R.F. 1992. Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. Boca Raton, FL: CRC Press.Google Scholar

Faber, G. 1923. Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt. Sitzungsber. Bayer. Akad. Wiss. Mnchen, Math.-Phys. Kl., 169–172.Google Scholar

Federer, H. 1959. Curvature measures. Trans. Amer. Math. Soc., 93, 418–491.Google Scholar

Federer, H. 1969. Geometric Measure Theory. Die Grundlehren der mathematischen Wissenschaften, Band 153. New York: Springer-Verlag New York Inc.Google Scholar

Federer, H., and Fleming, W.H. 1960. Normal and integral currents. Ann. of Math. (2), 72, 458–520.Google Scholar

Folland, G.B. 1999. Real Analysis: Modern Techniques and Their Applications. Second edition. Pure and Applied Mathematics (New York). New York: John Wiley & Sons Inc. A Wiley-Interscience Publication.Google Scholar

Folland, G.B. 2002. Advanced Calculus. Upper Saddle River, NJ: Prentice Hall.Google Scholar

Frostman, O. 1935. Potentiel d’équilibre et capacité de ensembles avec quelques applications à la théorie des fonctions. Med. Lund. Univ. Math. Sem., 3, 1–118.Google Scholar

Fuchs, W.H.J. 1963. Proof of a conjecture of G. Pólya concerning gap series. Illinois J. Math., 7, 661–667.Google Scholar

Fuchs, W.H.J. 1967. Developments in the classical Nevanlinna theory of meromorphic functions. Bull. Amer. Math. Soc., 73, 275–291.Google Scholar

Fuchs, W.H.J. 1974. A theorem on min_|z| log |f (z)|/T(r, f ). Pages 69–72. London Math. Soc. Lecture Note Ser., No. 12 of: Proceedings of the Symposium on Complex Analysis (Univ. Kent, Canterbury, 1973). London: Cambridge University Press.Google Scholar

Gardner, R.J. 2002. The Brunn–Minkowski inequality. Bull. Amer. Math. Soc. (N.S.), 39(3), 355–405.Google Scholar

Gehring, F.W. 1961. Symmetrization of rings in space. Trans. Amer. Math. Soc., 101, 499–519.Google Scholar

Gehring, F.W. 1962. Rings and quasiconformal mappings in space. Trans. Amer. Math. Soc., 103, 353–393.Google Scholar

Gilbarg, D., and Trudinger, N.S. 1983. Elliptic Partial Differential Equations of Second Order. Second edition. Grundlehren der Mathematischen Wissenschaften, vol. 224. Berlin: Springer-Verlag.Google Scholar

Giusti, E. 1984. Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol. 80. Basel: Birkhäuser Verlag.Google Scholar

Godula, J., and Nowak, M. 1987. Meromorphic univalent functions in an annulus. Rend. Circ. Mat. Palermo (2), 36(3), 474–481 (1988).Google Scholar

Goldberg, A.A., and Ostrovskii, I.V. 2008. Value Distribution of Meromorphic Functions. Translations of Mathematical Monographs, vol. 236. Translated from the 1970 Russian original by Mikhail Ostrovskii, With an appendix by Alexandre Eremenko and James K. Langley. Providence, RI: American Mathematical Society.Google Scholar

González, C. 2000. Differential inequalities associated with weighted symmetrization processes on the real line. J. Anal. Math., 82, 21–54.Google Scholar

Govorov, N.V. 1969. The Paley conjecture. Funkcional. Anal. i Priložen., 3(2), 41–45.Google Scholar

Gross, L. 1975. Logarithmic Sobolev inequalities. Amer. J. Math., 97(4), 1061–1083.Google Scholar

Hadwiger, H., and Ohmann, D. 1956. Brunn–Minkowskischer Satz und Isoperimetrie. Math. Z., 66, 1–8.Google Scholar

Haliste, K. 1965. Estimates of harmonic measures. Ark. Mat., 6, 1–31 (1965).Google Scholar

Hamel, F., Nadirashvili, N., and Russ, E. 2011. Rearrangement inequalities and applications to isoperimetric problems for eigenvalues. Ann. Math. (2), 174(2), 647–755.Google Scholar

Hardy, G.H., and Littlewood, J.E. 1930. A maximal theorem with function-theoretic applications. Acta Math., 54(1), 81–116.Google Scholar

Hardy, G.H., Littlewood, J.E., and Pólya, G. 1952. Inequalities. Second edition. Cambridge: Cambridge University Press.Google Scholar

Hayman, W.K. 1950. Symmetrization in the Theory of Functions. Tech. Rep. no. 11, Navy Contract N6-ori-106 Task Order 5. Stanford University.Google Scholar

Hayman, W.K. 1964. Meromorphic Functions. Oxford Mathematical Monographs. Oxford: Clarendon Press.Google Scholar

Hayman, W.K. 1967. Research Problems in Function Theory. London: The Athlone Press University of London.Google Scholar

Hayman, W.K. 1989. Subharmonic Functions. Vol. 2. London Mathematical Society Monographs, vol. 20. London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers].Google Scholar

Hayman, W.K. 1994. Multivalent Functions. Second edition. Cambridge Tracts in Mathematics and Mathematical Physics, No. 48. Cambridge: Cambridge University Press.Google Scholar

Hayman, W.K., and Kennedy, P.B. 1976. Subharmonic Functions. Vol. I. London Mathematical Society Monographs, No. 9. London: Academic Press [Harcourt Brace Jovanovich Publishers].Google Scholar

Hazewinkel, M. (ed.). 1995. Encyclopaedia of Mathematics. Translated from the Russian, Reprint of the 1988–1994 English translation. Dordrecht: Kluwer Academic Publishers.Google Scholar

Heinonen, J., Kilpeläinen, T., and Martio, O. 1993. Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Mathematical Monographs. New York: Clarendon Press.Google Scholar

Henrot, A. (ed). 2017. Shape Optimization and Spectral Theory. Warsaw: De Gruyter Open.Google Scholar

Herbst, I.W., and Zhao, Z.X. 1988. Sobolev spaces, Kac-regularity, and the Feynman–Kac formula. Pages 171–191 of: Seminar on Stochastic Processes, 1987 (Princeton, NJ, 1987). Progr. Probab. Statist., vol. 15. Boston: Birkhäuser Boston.Google Scholar

Hildén, K. 1976. Symmetrization of functions in Sobolev spaces and the isoperimetric inequality. Manuscripta Math., 18(3), 215–235.Google Scholar

Hoel, P.G., Port, S.C., and Stone, C.J. 1972. Introduction to Stochastic Processes. The Houghton Mifflin Series in Statistics. Boston.: Houghton Mifflin Co.Google Scholar

Hoffman, K. 1962. Banach Spaces of Analytic Functions. Prentice-Hall Series in Modern Analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc.Google Scholar

Hörmander, L. 1994. Notions of Convexity. Progress in Mathematics, vol. 127. Boston: Birkhäuser Boston Inc.Google Scholar

Iwaniec, T., and Manfredi, J.J. 1989. Regularity of p-harmonic functions on the plane. Rev. Mat. Iberoamericana, 5(1-2), 1–19.Google Scholar

Iwaniec, T., and Martin, G. 2001. Geometric Function Theory and Non-Linear Analysis. Oxford Mathematical Monographs. New York: Clarendon Press.Google Scholar

Jenkins, J.A. 1955. On circularly symmetric functions. Proc. Amer. Math. Soc., 6, 620–624.Google Scholar

Kac, M. 1949. On distributions of certain Wiener functionals. Trans. Amer. Math. Soc., 65, 1–13.Google Scholar

Karatzas, I., and Shreve, S.E. 1991. Brownian Motion and Stochastic Calculus. Second edition. Graduate Texts in Mathematics, vol. 113. New York: Springer-Verlag.Google Scholar

Kato, T. 1978. Trotter’s product formula for an arbitrary pair of self-adjoint contraction semigroups. Pages 185–195 of: Topics in Functional Analysis (Essays Dedicated to M. G. Kreĭn on the Occasion of his 70th Birthday). Adv. in Math. Suppl. Stud., vol. 3. New York: Academic Press.Google Scholar

Kawohl, B. 1985. Rearrangements and Convexity of Level Sets in PDE. Lecture Notes in Mathematics, vol. 1150. Berlin: Springer-Verlag.Google Scholar

Kellogg, O.D. 1967. Foundations of Potential Theory. Reprint from the first edition of 1929. Die Grundlehren der Mathematischen Wissenschaften, Band 31. Berlin: Springer-Verlag.Google Scholar

Kesavan, S. 2006. Symmetrization & Applications. Series in Analysis, vol. 3. Hacken-sack, NJ: World Scientific Publishing Co. Pte. Ltd.Google Scholar

Kirwan, W.E., and Schober, G. 1976. Extremal problems for meromorphic univalent functions. J. Anal. Math., 30, 330–348.Google Scholar

Köthe, G. 1960. Topologische lineare Räume. I. Die Grundlehren der mathematischen Wissenschaften, Bd. 107. Berlin: Springer-Verlag.Google Scholar

Krahn, E. 1925. Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises. Math. Ann., 94(1), 97–100.Google Scholar

Krzyż, J. 1959. Circular symmetrization and Green’s function. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys., 7, 327–330 (unbound insert).Google Scholar

Landkof, N.S. 1972. Foundations of Modern Potential Theory. Translated from the Russian by A.P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180. New York: Springer-Verlag.Google Scholar

Langford, J. J. 2015a. Neumann comparison theorems in elliptic PDEs. Potential Anal., 43(3), 415–459.Google Scholar

Langford, J.J. 2015b. Symmetrization of Poisson’s equation with Neumann boundary conditions. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 14(4), 1025–1063.Google Scholar

Laugesen, R. 1993. Extremal problems involving logarithmic and Green capacity. Duke Math. J., 70(2), 445–480.Google Scholar

Laugesen, R.S., and Morpurgo, C. 1998. Extremals for eigenvalues of Laplacians under conformal mapping. J. Funct. Anal., 155(1), 64–108.Google Scholar

Lebedev, N.N. 1972. Special Functions and Their Applications. Revised edition, translated from the Russian and edited by Silverman, R.A., Unabridged and corrected republication. New York: Dover Publications Inc.Google Scholar

Ledoux, M. 1994. Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space. Bull. Sci. Math., 118(6), 485–510.Google Scholar

Lehto, O. 1953. A majorant principle in the theory of functions. Math. Scand., 1, 5–17.Google Scholar

Lehto, O., and Virtanen, K.I. 1973. Quasiconformal Mappings in the Plane. Second edition. Translated from the German by K. W. Lucas, Die Grundlehren der mathematischen Wissenschaften, Band 126. New York: Springer-Verlag.Google Scholar

Leung, Y.J. 1979. Integral means of the derivatives of some univalent functions. Bull. London Math. Soc., 11(3), 289–294.Google Scholar

Levin, B.J. 1980. Distribution of Zeros of Entire Functions. Revised edition. Translations of Mathematical Monographs, vol. 5. Translated from the Russian by R.P. Boas, J.M. Danskin, F.M. Goodspeed, J. Korevaar, A.L. Shields and H.P. Thielman. Providence, RI: American Mathematical Society.Google Scholar

Lieb, E.H. 1976–1977. Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Studies Appl. Math., 57(2), 93–105.Google Scholar

Lieb, E.H. 1983. Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities. Ann. Math. (2), 118(2), 349–374.Google Scholar

Lieb, E.H. 1990. Gaussian kernels have only Gaussian maximizers. Invent. Math., 102(1), 179–208.Google Scholar

Lieb, E.H., and Loss, Michael. 1997. Analysis. Graduate Studies in Mathematics, vol. 14. Providence, RI: American Mathematical Society.Google Scholar

Littlewood, J.E. 1944. Lectures on the Theory of Functions. London: Oxford University Press.Google Scholar

Littman, W. 1959. A strong maximum principle for weakly L-subharmonic functions. J. Math. Mech., 8, 761–770.Google Scholar

Lumiste, Ü., and Peetre, J. (eds.). 1994. Edgar Krahn, 1894–1961. Amsterdam: IOS Press.Google Scholar

Luttinger, J.M. 1973a. Generalized isoperimetric inequalities. J. Math. Phys., 14, 586–593.Google Scholar

Luttinger, J.M. 1973b. Generalized isoperimetric inequalities. II, III. J. Math. Phys., 14, 1444–1447, 1448–1450.Google Scholar

Marshall, A.W., Olkin, I., and Arnold, B.C. 2011. Inequalities: Theory of Majorization and Its Applications. Second edition. Springer Series in Statistics. New York: Springer.Google Scholar

Marshall, D.E. 1989. A new proof of a sharp inequality concerning the Dirichlet integral. Ark. Mat., 27(1), 131–137.Google Scholar

Mattila, P. 1995. Geometry of Sets and Measures in Euclidean Spaces. Cambridge Studies in Advanced Mathematics, vol. 44. Cambridge: Cambridge University Press.Google Scholar

Maz’ja, V.G. 1985. Sobolev Spaces. Springer Series in Soviet Mathematics. Translated from the Russian by T. O. Shaposhnikova. Berlin: Springer-Verlag.Google Scholar

McCann, R.J. 1995. Existence and uniqueness of monotone measure-preserving maps. Duke Math. J., 80(2), 309–323.Google Scholar

McCann, R.J. 2001. Polar factorizat3ion of maps on Riemannian manifolds. Geom. Funct. Anal., 11(3), 589–608.Google Scholar

McKean, H.P. 1973. Geometry of differential space. Ann. Prob., 1, 197–206.Google Scholar

McKean, Jr., H.P., and Singer, I.M. 1967. Curvature and the eigenvalues of the Laplacian. J. Differential Geometry, 1(1), 43–69.Google Scholar

Méndez-Hernández, P. J. 2006. An isoperimetric inequality for Riesz capacities. Rocky Mountain J. Math., 36(2), 675–682.Google Scholar

Mori, A. 1956. On an absolute constant in the theory of quasi-conformal mappings. J. Math. Soc. Japan, 8, 156–166.Google Scholar

Morpurgo, C. 2002. Sharp inequalities for functional integrals and traces of conformally invariant operators. Duke Math. J., 114(3), 477–553.Google Scholar

Morrey, Jr., C.B. 1938. On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc., 43(1), 126–166.Google Scholar

Morrey, Jr., C.B. 1940. Existence and differentiability theorems for the solutions of variational problems for multiple integrals. Bull. Amer. Math. Soc., 46, 439–458.Google Scholar

Moser, J. 1970/71. A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J., 20, 1077–1092.Google Scholar

Mostow, G.D. 1968. Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms. Inst. Hautes Études Sci. Publ. Math., 53–104.Google Scholar

Nadirashvili, N.S. 1993. An isoperimetric inequality for the main frequency of a clamped plate. Dokl. Akad. Nauk, 332(4), 436–439.Google Scholar

Nelson, E. 1973. The free Markoff field. J. Funct. Anal., 12, 211–227.Google Scholar

Nevanlinna, R. 1970. Analytic Functions. Translated from the second German edition by Phillip Emig. Die Grundlehren der mathematischen Wissenschaften, Band 162. Springer-Verlag: New York-Berlin.Google Scholar

Onofri, E. 1982. On the positivity of the effective action in a theory of random surfaces. Comm. Math. Phys., 86(3), 321–326.Google Scholar

Osgood, B., Phillips, R., and Sarnak, P. 1988. Extremals of determinants of Laplacians. J. Funct. Anal., 80(1), 148–211.Google Scholar

Osserman, R. 1978. The isoperimetric inequality. Bull. Amer. Math. Soc., 84(6), 1182–1238.Google Scholar

Paouris, G., and Pivovarov, P. 2012. A probabilistic take on isoperimetric-type inequalities. Adv. Math., 230(3), 1402–1422.Google Scholar

Paouris, G., and Pivovarov, P. 2017. Random ball-polyhedra and inequalities for intrinsic volumes. Monatsh. Math., 182(3), 709–729.Google Scholar

Payne, L.E. 1967. Isoperimetric inequalities and their applications. SIAM Rev., 9, 453–488.Google Scholar

Payne, L.E., Pólya, G., and Weinberger, H.F. 1955. Sur le quotient de deux fréquences propres consécutives. C. R. Acad. Sci. Paris, 241, 917–919.Google Scholar

Peretz, R. 2017. Applications of Steiner symmetrization to some extremal problems in geometric function theory. WSEAS Trans. Math., 16, 350–367.Google Scholar

Petrenko, V.P. 1969. Growth of meromorphic functions of finite lower order. Izv. Akad. Nauk SSSR Ser. Mat., 33, 414–454.Google Scholar

Pfiefer, R.E. 1990. Maximum and minimum sets for some geometric mean values. J. Theoret. Probab., 3(2), 169–179.Google Scholar

Pfluger, A. 1946. Zur Defektrelation ganzer Funktionen endlicher Ordnung. Comment. Math. Helv., 19, 91–104.Google Scholar

Pichorides, S.K. 1972. On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov. Studia Math., 44, 165–179. (errata insert). Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, II.Google Scholar

Pitt, L.D. 1977. A Gaussian correlation inequality for symmetric convex sets. Ann. Prob., 5(3), 470–474.Google Scholar

Poincaré, H. 1887. Sur un théorème de M. Liapounoff, relatif à l’équilibre d’une masse fluide. Comptes Rendus hebdomadaires des séances de l’Académie des Sciences, 104, 622–625.Google Scholar

Pólya, G., and Szegő, G. 1945. Inequalities for the capacity of a condenser. Amer. J. Math., 67, 1–32.Google Scholar

Pólya, G., and Szegő, G. 1951. Isoperimetric Inequalities in Mathematical Physics. Annals of Mathematics Studies, no. 27. Princeton, NJ: Princeton University Press.Google Scholar

Pólya, G. 1948. Torsional rigidity, principal frequency, electrostatic capacity and symmetrization. Quart. Appl. Math., 6, 267–277.Google Scholar

Pólya, G. 1950. Sur la symétrisation circulaire. C.R. Acad. Sci. Paris, 230, 25–27.Google Scholar

Pólya, G. 1984. Collected Papers. Vol. III. Mathematicians of Our Time, vol. 21. Analysis, Edited by Hersch, J., Rota, G.-C., Reynolds, M.C. and Shortt, R.M.. Cambridge, MA: MIT Press.Google Scholar

Pruss, A.R. 1996. Three counterexamples for a question concerning Green’s functions and circular symmetrization. Proc. Amer. Math. Soc., 124(6), 1755–1761.Google Scholar

Ransford, T. 1995. Potential Theory in the Complex Plane. London Mathematical Society Student Texts, vol. 28. Cambridge: Cambridge University Press.Google Scholar

Rayleigh, Baron, J.W. 1945. The Theory of Sound. Second edition. New York: Dover Publications.Google Scholar

Reed, M., and Simon, B. 1972. Methods of Modern Mathematical Physics. I. Functional Analysis. New York: Academic Press.Google Scholar

Reed, M., and Simon, B. 1975. Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness. New York: Academic Press [Harcourt Brace Jovanovich Publishers].Google Scholar

Reshetnyak, Y.G. 1989. Space Mappings with Bounded Distortion. Translations of Mathematical Monographs, vol. 73. Translated from the Russian by H.H. McFaden. Providence, RI: American Mathematical Society.Google Scholar

Rickman, S. 1993. Quasiregular Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 26. Berlin: Springer-Verlag.Google Scholar

Riesz, F. 1930. Sur une inégalité intégrale. J. London Math. Soc., 5(3), 162–168.Google Scholar

Riesz, M. 1928. Sur les fonctions conjuguées. Math. Z., 27(1), 218–244.Google Scholar

Roberts, A.W., and Varberg, D.E. 1973. Convex Functions. Pure and Applied Mathematics, Vol. 57. New York–London: Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers].Google Scholar

Rogers, C.A. 1957. A single integral inequality. J. London Math. Soc., 32, 102–108.Google Scholar

Rossi, J., and Weitsman, A. 1983. A unified approach to certain questions in value distribution theory. J. London Math. Soc. (2), 28(2), 310–326.Google Scholar

Royen, T. 2014. A simple proof of the Gaussian correlation conjecture extended to some multivariate gamma distributions. Far East J. Theor. Stat., 48(2), 139–145.Google Scholar

Rudin, W. 1964. Principles of Mathematical Analysis. Second edition. New York: McGraw-Hill Book Co.Google Scholar

Rudin, W. 1966. Real and Complex Analysis. New York: McGraw-Hill Book Co.Google Scholar

Ryff, J.V. 1970. Measure preserving transformations and rearrangements. J. Math. Anal. Appl., 31, 449–458.Google Scholar

Sarvas, J. 1972. Symmetrization of condensers in n-space. Ann. Acad. Sci. Fenn. Ser. A I, 44.Google Scholar

Schaefer, H.H. 1971. Topological Vector Spaces. Third printing corrected, Graduate Texts in Mathematics, Vol. 3. New York: Springer-Verlag.Google Scholar

Schechtman, G., Schlumprecht, T., and Zinn, J. 1998. On the Gaussian measure of the intersection. Ann. Prob., 26(1), 346–357.Google Scholar

Schmidt, E. 1943. Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionenzahl. Math. Z., 49, 1–109.Google Scholar

Schneider, R. 1993. Convex Bodies: The Brunn–Minkowski Theory. Encyclopedia of Mathematics and Its Applications, vol. 44. Cambridge: Cambridge University Press.Google Scholar

Schulz, F., and Vera de Serio, V. 1993. Symmetrization with respect to a measure. Trans. Amer. Math. Soc., 337(1), 195–210.Google Scholar

Schwarz, H.A. 1884. Beweis des Satzes, dass die Kugel kleinere Oberfläche besitzt, als jeder andere Körper gleichen Volumens. Nachrichten Königlichen Gesellschaft Wissenschaften Göttingen, 1–13.Google Scholar

Schwarz, H.A. 1890. Gesammelte Mathematische Abhandlungen. Berlin: Springer Verlag.Google Scholar

Shea, D. F. 1966. On the Valiron deficiencies of meromorphic functions of finite order. Trans. Amer. Math. Soc., 124, 201–227.Google Scholar

Sierpiński, W. 1920. Sur la question de la mesurabilité de la base de M. Hamel. Fundamenta Mathematicae, 1(1), 105–111.Google Scholar

Simon, B. 1979. Functional Integration and Quantum Physics. Pure and Applied Mathematics, vol. 86. New York: Academic Press Inc. [Harcourt Brace Jovanovich Publishers].Google Scholar

Simon, B., and Høegh-Krohn, R. 1972. Hypercontractive semigroups and two dimensional self-coupled Bose fields. J. Funct. Anal., 9, 121–180.Google Scholar

Smith, K.T. 1983. Primer of Modern Analysis. Second edition. Undergraduate Texts in Mathematics. New York: Springer-Verlag.Google Scholar

Sobolev, S.L. 1938. On a theorem in functional analysis. Sb. Math., 4, 471–497.Google Scholar

Solynin, A.Y. 1996. Extremal configurations in some problems on capacity and harmonic measure. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 226 (Anal. Teor. Chisel i Teor. Funktsiĭ. 13), 170–195, 239.Google Scholar

Sperner, Jr., E. 1973. Zur Symmetrisierung von Funktionen auf Sphären. Math. Z., 134, 317–327.Google Scholar

Sperner, Jr., E. 1979. Symmetrization and currents. Mathematika, 26(2), 269–289 (1980).Google Scholar

Spivak, M. 1965. Calculus on Manifolds. A Modern Approach to Classical Theorems of Advanced Calculus. New York-Amsterdam: W. A. Benjamin, Inc.Google Scholar

Stammbach, U. 2012. A letter of Hermann Amandus Schwarz on isoperimetric problems. Math. Intelligencer, 34(1), 44–51. With an appendix containing German transcription of the letter.Google Scholar

Stanoyevitch, A. 1994. Integral inequalities and equalities for the rearrangement of Hardy and Littlewood. J. Math. Anal. Appl., 183(3), 509–517.Google Scholar

Stein, E.M. 1970. Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No. 30. Princeton, NJ: Princeton University Press.Google Scholar

Stein, E.M., and Weiss, G. 1971. Introduction to Fourier Analysis on Euclidean Spaces. Princeton Mathematical Series, No. 32. Princeton, NJ: Princeton University Press.Google Scholar

Steiner, J. 1842. Sur le maximum et le minimum des figures dans le plan, sur la sphère et dans l’espace en géneral. J. Reine Angew. Math., 24, 93–152.Google Scholar

Steiner, J. 1882. Gesammelte Werke Vol.2. New York: Prussian Academy of Sciences.Google Scholar

Stroock, D.W. 1993. Probability Theory, An Analytic View. Cambridge: Cambridge University Press.Google Scholar

Szegő, G. 1930. Über einige Extremalaufgaben der Potentialtheorie. Math. Z., 31(1), 583–593.Google Scholar

Szegö, G. 1950. On membranes and plates. Proc. Natl. Acad. Sci. U.S.A., 36, 210–216.Google Scholar

Szegö, G. 1958. Note to my paper “On membranes and plates”. Proc. Natl. Acad. Sci. U.S.A., 44, 314–316.Google Scholar

Talenti, G. 1976a. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. (4), 110, 353–372.Google Scholar

Talenti, G. 1976b. Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 3(4), 697–718.Google Scholar

Talenti, G. 1979. Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces. Ann. Mat. Pura Appl. (4), 120, 160–184.Google Scholar

Talenti, G. 1993. The standard isoperimetric theorem. Pages 73–123 of: Handbook of Convex Geometry, Vol. A, B. Amsterdam: North-Holland.Google Scholar

Talenti, G. 1997. A weighted version of a rearrangement inequality. Ann. Univ. Ferrara Sez. VII (N.S.), 43, 121–133 (1998).Google Scholar

Talenti, G. 2016. The art of rearranging. Milan J. Math., 84(1), 105–157.Google Scholar

Teichmüller, O. 1939. Vermutungen und Sätze über die Wertverteilung gebrochener Funktionen endlicher Ordnung. Deutsche Math., 4, 163–190.Google Scholar

Tikhomirov, V.M. 1990. Stories about Maxima and Minima. Mathematical World, vol. 1. Translated from the 1986 Russian original by Abe Shenitzer. Providence, RI: American Mathematical Society.Google Scholar

Tsuji, M. 1975. Potential Theory in Modern Function Theory. Reprinting of the 1959 original. New York: Chelsea Publishing Co.Google Scholar

Väisälä, J. 1961. On quasiconformal mappings in space. Ann. Acad. Sci. Fenn. Ser. A I No., 298, 36.Google Scholar

Van Schaftingen, J. 2006. Approximation of symmetrizations and symmetry of critical points. Topol. Methods Nonlinear Anal., 28(1), 61–85.Google Scholar

Vilenkin, N.J. 1968. Special Functions and the Theory of Group Representations. Translated from the Russian by V.N. Singh. Translations of Mathematical Monographs, Vol. 22. Providence, RI: American Mathematical Society.Google Scholar

Vilenkin, N.J., and Klimyk, A.U. 1991. Representation of Lie Groups and Special Functions. Vol. 1. Mathematics and its Applications (Soviet Series), vol. 72. Simplest Lie groups, special functions and integral transforms, Translated from the Russian by V.A. Groza and A.A. Groza. Dordrecht: Kluwer Academic Publishers Group.Google Scholar

Villani, C. 2003. Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58. Providence, RI: American Mathematical Society.Google Scholar

Watanabe, T. 1983. The isoperimetric inequality for isotropic unimodal Lévy processes. Z. Wahrsch. Verw. Gebiete, 63(4), 487–499.Google Scholar

Weitsman, A. 1979. A symmetry property of the Poincaré metric. Bull. London Math. Soc., 11(3), 295–299.Google Scholar

Weitsman, A. 1986. Symmetrization and the Poincaré metric. Ann. Math. (2), 124(1), 159–169.Google Scholar

Wojtaszczyk, P. 1991. Banach Spaces for Analysts. Cambridge Studies in Advanced Mathematics, vol. 25. Cambridge: Cambridge University Press.Google Scholar

Wolontis, V. 1952. Properties of conformal invariants. Amer. J. Math., 74, 587–606.Google Scholar

Wu, J.-M. 2002. Harmonic measures for symmetric stable processes. Studia Math., 149(3), 281–293.Google Scholar

Yanagihara, H. 1993. An integral inequality for derivatives of equimeasurable rearrangements. J. Math. Anal. Appl., 175(2), 448–457.Google Scholar

Yang, S.S. 1994. Estimates for coefficients of univalent functions from integral means and Grunsky inequalities. Israel J. Math., 87(1–3), 129–142.Google Scholar

Ziemer, W.P. 1989. Weakly Differentiable Functions. Graduate Texts in Mathematics, vol. 120. New York: Springer-Verlag.Google Scholar

Zygmund, A. 1968. Trigonometric Series: Vols. I, II. Second edition, reprinted with corrections and some additions. London: Cambridge University Press.Google Scholar