Extension of \(CR\) structures on three dimensional compact pseudoconvex CR manifolds
type: Item
instance of: scholarly article
title: Extension of \(CR\) structures on three dimensional compact pseudoconvex CR manifolds
zbMATH Open document ID: 1090.32022
published in: Mathematische Annalen
publication date: 2006-03-21T00:00:00Z
review text: The authors discuss the extension of CR structures for orientable abstract CR manifolds \(M\) of hypersurface type of real dimension \(3\). First they prove (Theorem 1.1) that if there exists a smooth real valued function \(\lambda\) on \(M\) which is strictly subharmonic at all points where the Levi form of \(M\) is zero, then \(M\) is a pseudo-concave component of the boundary \(\partial\Omega\) of a \(2\)-dimensional complex manifold with boundary. This extends a result of \textit{M. Christ} [Ann. Math. (2) 129, No. 1, 195--213 (1989; Zbl 0668.32019)] for an \(M\) of finite type. In case an extension to the \textit{pseudo-convex} side is already given, the assumptions of Theorem 1.1 yield an embedding of \(M\) into a \(2\)-dimensional complex manifold. Straightening the pseudo-convexity assumption for the CR structure, the authors obtain a local version of these results, that also applies to non-compact CR manifolds \(M\).
reviewed by: Mauro Nacinovich
Mathematics Subject Classification ID: 32V30
Mathematics Subject Classification ID: 32G07
Mathematics Subject Classification ID: 32W05
zbMATH DE Number: 5013662
zbMATH Keywords: CR manifolds
zbMATH Keywords: pseudo-convex manifolds
zbMATH Keywords: CR structures
author: David W. Catlin
author: Sanghyun Cho
MaRDI profile type: Publication
full work available at URL: s00208-005-0716-5
OpenAlex ID: W1978096973
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DOI: 10.1007/S00208-005-0716-5
description: scientific article; zbMATH DE number 5013662