Aneurysms of pseudoconcave \(CR\) manifolds
type: Item
instance of: scholarly article
title: Aneurysms of pseudoconcave \(CR\) manifolds
zbMATH Open document ID: 0843.32011
DOI: 10.1007/BF02572620
author: Mauro Nacinovich
author: Clyde Denson Hill
published in: Mathematische Zeitschrift
publication date: 1996-08-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174815
review text: Aneurysms are for higher codimensional \(CR\) manifolds the analogue of the bumps used by A. Andreotti and H. Grauert to prove finiteness theorems for the Dolbeault cohomology of bounded domains in a complex manifold. The study of these objects permits us to solve the Cauchy problem for cohomology classes of \(CR\) manifold \(M\) of type \((n,k)\) which is \(q\)-pseudoconcave and generically embedded in its tubular neighborhood. As an application we obtain results on the finiteness of the global \(\overline{\partial}_M\)-cohomology groups in dimension \(> n - q\) and the infinite dimensionality in dimension \(= n - q\) suitable pseudoconvexity assumptions at infinity, complementing those obtained by the authors in `Pseudoconcave \(CR\) manifolds', preprint Dip. Mat. Univ. Pisa 1.76(723), feb.(1993). When \(M\) is compact, we obtain a comparison between the \(\overline{\partial}_M\)-cohomology and Čech cohomology groups with coefficients in the sheaf of \(CR\) forms.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 55N05
zbMATH DE Number: 856570
zbMATH Keywords: pseudoconcave CR manifolds
zbMATH Keywords: finiteness
zbMATH Keywords: \(\overline{\partial}_ M\)-cohomology
zbMATH Keywords: Čech cohomology
MaRDI profile type: Publication
cites work: Q3940208
cites work: Théorèmes de finitude pour la cohomologie des espaces complexes
cites work: Q5670927
cites work: Complexes of differential operators. The Mayer-Vietoris sequence
cites work: Q5535139
cites work: Holomorphic extension of CR functions
cites work: Q4276582
cites work: Q4874422
cites work: Q4201954
cites work: Q5566770
cites work: Poincaré lemma for tangential Cauchy Riemann complexes
cites work: On strict Levi q-convexity and q-concavity on domains with piecewise smooth boundaries
cites work: Tangential Cauchy-Riemann complexes on distributions
description: scientific article; zbMATH DE number 856570