Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-24T16:08:17.576Z Has data issue: false hasContentIssue false
  • English
  • Français

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, Christine.Laurent@ujf-grenoble.fr
Jürgen Leiterer
Affiliation:
Institut für Mathematik, Humboldt-Universität, Ziegelstrasse 13A, D-10117 Berlin (Allemagne), Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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