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On the cohomological completeness of q-complete domains with corners

Published online by Cambridge University Press:  22 January 2016

Kazuko Matsumoto
Kazuko Matsumoto*
Affiliation:
Department of Applied Mathematics, Osaka Women’s University, Daisen-cho, Sakai 590-0035, Japan, kazuko@appmath.osaka-wu.ac.jp
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Abstract

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We prove the vanishing and non-vanishing theorems for an intersection of a finite number of q-complete domains in a complex manifold of dimension n. When q does not divide n, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for q-convex functions with corners and the vanishing theorem of Andreotti-Grauert for q-complete domains. We also give an example which implies our result is best possible.

Keywords

32F10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 105 - 112
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[A-G] Andreotti, A. and Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193–259.Google Scholar
[D-F] Diederich, K. and Fornaess, J. E., Smoothing q-convex functions and vanishing theorems, Invent. Math., 82 (1985), 291–305.CrossRefGoogle Scholar
[E-S] Eastwood, G. M. and Suria, G. V., Cohomologically complete and pseudoconvex domains, Comment. Math. Helv., 55 (1980), 413–426.Google Scholar
[G-W] Greene, E. R. and Wu, H., Embedding of open Riemannian manifolds by harmonic functions, Ann. Inst. Fourier (Grenoble), 25 (1975), 215–235.Google Scholar
[M-1] Matsumoto, K., Pseudoconvex domains of general order in Stein manifolds, Mem. Fac. Sci. Kyushu Univ., 43 (1989), 67–76.Google Scholar
[M-2] Matsumoto, K., Boundary distance functions and q-convexity of pseudoconvex domains of general order in Kähler manifolds, J. Math. Soc. Japan, 48 (1996), 85–107.Google Scholar
[S-V] Sorani, G. and Villani, V., q-complete spaces and cohomology, Trans. Amer. Math. Soc, 125 (1966), 432–448.Google Scholar
[W] Watanabe, K., Pseudoconvex domains of general order and vanishing cohomology, Kobe J. Math., 10 (1993), 107–115.Google Scholar