Nagoya Mathematical Journal

Malgrange's vanishing theorem in 1-concave CR manifolds

Christine Laurent-Thiébaut and Jürgen Leiterer

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We prove a vanishing theorem for the $\overline{\partial_b}$-cohomology in top degree on 1-concave $CR$ generic manifolds.

Article information

Nagoya Math. J., Volume 157 (2000), 59-72.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32L20: Vanishing theorems
Secondary: 32C35: Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30] 32V20: Analysis on CR manifolds


Laurent-Thiébaut, Christine; Leiterer, Jürgen. Malgrange's vanishing theorem in 1-concave CR manifolds. Nagoya Math. J. 157 (2000), 59--72.

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  • R.A. Airapetjan, G.M. Henkin, Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of $CR$-functions , Russian Math. Survey, 39 (1984), 41–118.
  • M.Y. Barkatou, Optimal regularity for $\pa_b$ on $CR$ manifolds , Prépublication de l'Institut Fourier, 374, 1997 , to appear in Journal of Geometric Analysis 2.
  • L. De Carli, M. Nacinovich, Unique continuation in abstract pseudoconcave $CR$-manifolds , Preprint Dipartimento di Matematica, Pisa 1. 177. 1028, April 1997.
  • R.E. Green, H. Wu, Embedding of open Riemannian manifolds by harmonic functions , \aif, 25 (1975), 215–235.
  • V. Guillemin, A. Pollack, Differential Topology, Prentice-Hall (1974).
  • G.M. Henkin, Solution des équations de Cauchy-Riemann tangentielles sur des variétés de Cauchy-Riemann $q$-convexes , \cras, 292 (1981), 27–30.
  • ––––, The Hartogs-Bochner effect on $CR$ manifolds , Soviet. Math. Dokl., 29 (1984), 78–82.
  • G.M. Henkin, J. Leiterer, Theory of functions on complex manifolds, Birkhäuser Verlag (1984).
  • C.D. Hill, M. Nacinovich, Pseudoconcave $CR$ manifolds , Complex Analysis and Geometry, Lecture Notes in Pure and Appl. Math., 173, Marcel Dekker, New York (1996), 275–297.
  • J.-J. Kohn, H. Rossi, On the extension of holomorphic functions from the boundary of a complex manifold , Ann. of Math., 81 (1965), 451–472.
  • Ch. Laurent-Thiébaut, Résolution du $\pa_b$ $\grave{a}$ support compact et phénom$\grave{e}$ne de Hartogs-Bochner dans les variétés $CR$ , Proc. of Symp. in Pure Math., 52 (1991), 239–249.
  • Ch. Laurent-Thiébaut, J. Leiterer, Andreotti-Grauert theory on real hypersurfaces, Quaderni della Scuola Normale Superiore di Pisa (1995).
  • B. Malgrange, Faisceaux sur des variétés analytiques réelles , Bull. Soc. Math. de France, 85 (1957), 231–237.
  • A.E. Tumanov, Extension of $CR$ functions into a wedge from a manifold of finite type , Math. USSR - Sb -, 64 (1989), 129–140.