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Some applications of Serre duality in CR manifolds

Published online by Cambridge University Press:  22 January 2016

Christine Laurent-Thiébaut  and
Jürgen Leiterer
Christine Laurent-Thiébaut
Affiliation:
Institut Fourier, UMR 5582 CNRS-UJF, Laboratoire de Mathématiques, Université Grenoble 1, B.P. 74, F-38402 St-Martin d’Héres Cedex, France, [email protected]
Jürgen Leiterer
Affiliation:
Institut für Mathematik, Humboldt-Universität, Ziegelstrasse 13A, D-10117 Berlin (Allemagne), Germany
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Abstract

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Applying the methods of Serre duality in the setting of CR manifolds we prove approximation theorems and we study the Hartogs-Bochner phenomenon in 1-concave CR generic manifolds.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 154 , 1999 , pp. 141 - 156
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[1] Airapetjan, R. A. and Henkin, B. M., Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions, Russian Math. Survey, 39 (1984), 41–118.Google Scholar
[2] Airapetjan, R. A. and Henkin, B. M., Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions II, Math. USSR Sbornik, 55 (1986), 91–111.Google Scholar
[3] Andreotti, A. and Kas, A., Duality on complex spaces, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 187–263.Google Scholar
[4] Andreotti, A., Fredricks, G. A. and Nacinovich, M., On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes, Ann. Scuola Norm. Sup. Pisa, 8 (1981), 365–404.Google Scholar
[5] Barkatou, M. Y., Optimal regularity of on CR manifolds, Prépublication de l’Institut Fourier, 374 (1997).Google Scholar
[6] Barkatou, M. Y., Some applications of a new integral formula for , to appear.CrossRefGoogle Scholar
[7] Boggess, A., CR manifolds and the tangential Cauchy-Riemann complex, CRC Press, Boca Raton, Florida, 1991.Google Scholar
[8] Cassa, A., Coomologia separata sulle varietà analitiche complesse, Ann. Scuola Norm. Sup. Pisa (3), 25 (1971), 290–323.Google Scholar
[9] Grothendieck, A., Espaces vectoriels topologiques, Societate de matematica de Sao Paulo, 1958.Google Scholar
[10] Henkin, G. M., Solution des équations de Cauchy-Riemann tangentielles sur des variétés de Cauchy-Riemann q-convexes, C. R. Acad. Sci. Paris Sér. I Math., 292 (1981), 27–30.Google Scholar
[11] Henkin, G. M., The Hartogs-Bochner effect on CR manifolds, Soviet. Math. Dokl., 29 (1984), 78–82.Google Scholar
[12] Hill, C. D. and Nacinovich, M., Pseudoconcave CR manifolds, Complex Analysis and Geometry, Lecture Notes in Pure and Appl. Math., 173, Marcel Dekker, New York (1996), 275–297.Google Scholar
[13] Hill, C. D. and Nacinovich, M., Duality and distribution cohomology of CR manifolds, Ann. Scuola Norm. Sup. Pisa, serie IV, 22 (1995).Google Scholar
[14] Hörmander, L., An introduction to complex analysis in several variables, 2nd ed. North Holland Publishing co., Amsterdam, 1973.Google Scholar
[15] Hörmander, L. and Wermer, J., Uniform approximation on compact subsets in ℂn , Math. Scand., 26 (1968), 5–21.Google Scholar
[16] Kohn, J.-L. and Rossi, H., On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math., 81 (1965), 451–472.Google Scholar
[17] Laurent-Thiébaut, Ch., Résolution du à support compact et phénomène de Hartogs-Bochner dans les variétés CR, Proc. of Symp. in Pure Math., 52 (1991), 239–249.Google Scholar
[18] Laurent-Thiéebaut, Ch. and Leiterer, J., Andreotti-Grauert theory on real hypersurfaces, Quaderni della Scuola Normale Superiore di Pisa, 1995.Google Scholar
[19] Laurent-Thiéebaut, Ch. and Leiterer, J., Malgrange’s vanishing theorem in 1-concave CR manifolds, Prépublication de l’Institut Fourier, Grenoble, 395 (1997), to appear in Nagoya Math. J.Google Scholar
[20] Nacinovich, M., Poincaré lemma for tangential Cauchy-Riemann complexes, Math. Ann., 281 (1988), 459–482.Google Scholar
[21] Serre, J.-P., Un théorème de dualité, Comm. Math. Helvetici, 29 (1955), 9–26.Google Scholar
[22] Treves, F., Topological vector spaces, distributions and kernels, Academic Press, New-York, London, 1967.Google Scholar
[23] Weinstock, B. M., Continuous boundary values of analytic functions of several complex variables, Proc. Amer. Math. Soc., 21 (1969), 463–466.CrossRefGoogle Scholar