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On the bergman kernel of hyperconvex domains

Published online by Cambridge University Press:  22 January 2016

Takeo Ohsawa*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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Let D be a bounded pseudoconvex domain in Cn, and let KD (z, w) be the Bergman kernel function of D. The boundary behavior of KD (z, w), or that of KD (z, z), has attracted a lot of attention because it is closely related to the pseudoconformal geometry of D and ∂D.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[C] Catlin, D., Subelliptic estimates for the -Neumann problem on pseudoconvex domains, Ann. of Math., 126 (1986), 131191.Google Scholar
[De] Demailly, J. P., Estimation L 2 pour l’operateur d’un fibre vectoriel holomorphe semi-positif au-dessus d’une variété kãhlérienne complète, Ann. sc. Ec. Norm. Sup., 15 (1982), 457511.Google Scholar
[D] Diederich, K., Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudokonvexen Gebieten, Math. Ann., 189 (1970), 936.Google Scholar
[D-H-O] Diedreich, K., Herbort, G. and Ohsawa, T., The Bergman kernel on uniformly extendable pseudoconvex domains, Math. Ann., 273 (1986), 471478.Google Scholar
[E] Earle, C. J., On the Carathéodory metric in Teichmüller spaces, in Discontinuous groups and Riemann surfaces, Ann. Math. Stud., 79, Princeton University Press, 1974.Google Scholar
[F-K] Farkas, H. M. and Kra, I., Riemann surfaces, Springer-Verlag, 1991.Google Scholar
[F] Fefferman, C., The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26 (1974), 165.Google Scholar
[H] Hayman, W. K., Subharmonic functions Vol. 2, London Math. Soc. Monograph No. 20, Academic Press 1989.Google Scholar
[Hö] Hörmander, L., L 2-estimates and existence theorems for the -operator, Acta Math., 113 (1965), 89152.Google Scholar
[Kr] Krushkal’, S. L., Strengthening pseudoconvexity of finite-dimensional Teichmüller spaces, Math. Ann., 290 (1991), 681687.Google Scholar
[O-1] Ohsawa, T., Boundary behavior of the Bergman kernel function on pseudoconvex domains, Publ. RIMS, Kyoto Univ., 20 (1984), 897902.Google Scholar
[O-2] Ohsawa, T., Vanishing theorems on complete Kãhler manifolds, Publ. RIMS, Kyoto Univ., 20 (1984), 2138.Google Scholar
[O-3] Ohsawa, T., On the extension of L 2 holomorphic functions II, Publ. RIMS, Kyoto Univ., 24 (1988), 265274.Google Scholar
[O-T] Ohsawa, T. and Takegoshi, K., On the extension of L 2 holomorphic functions, Math. Z., 197 (1988), 112.Google Scholar
[P] Poincaré, H., Théorie du potentiel Newtonien, Leçons professées à la Sorbonne, Paris, 1899.Google Scholar
[S] Stehlé, J. L., Fonctions plurisubharmoniques et convexite holomorphe de certaines fibrès analytiques, C. R. Hebd. Acad. Sci. Ser. A-B 279 (1964), 235238.Google Scholar
[W] Wiener, N., Certain notions in potential theory, J. Math. Mass. Inst. Tech., 3 (1924), 2451.Google Scholar
[Z] Zalcman, L., Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc., 144 (1969), 241269.Google Scholar