Deformation of CR-manifolds, minimal points and CR-manifolds with the microlocal analytic extension property
type: Item
instance of: scholarly article
title: Deformation of CR-manifolds, minimal points and CR-manifolds with the microlocal analytic extension property
zbMATH Open document ID: 0917.32007
DOI: 10.1007/BF02921623
published in: The Journal of Geometric Analysis
publication date: 1998-11-05T00:00:00Z
review text: If \(M\) is a smooth CR-manifold (embedded) and \(p\) is a point in \(M\), the author shows how one can deform \(M\) into a smooth CR-manifold \(M_{d}\), letting fixed all the points outside a small truncated cone with vertex in \(p\), such that \(p\) is a minimal point of \(M_{d}\). Thus one is able to get a new proof of the fact that wedge extendability of continuous CR-functions propagates along the CR-orbits of a CR-manifold. The author also shows that if \(M\) is a connected generic (embedded) CR-manifold, each continuous function on \(M\) is a continuous CR-function iff its restriction to each CR-orbit of \(M\) is a CR-function on the orbit. If \(M\) consists of a single orbit, then each continuous CR-function on \(M\) is wedge extendable at any point of \(M\).
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 32G07
zbMATH DE Number: 1191284
zbMATH Keywords: CR-orbits
zbMATH Keywords: minimal point
zbMATH Keywords: analytic extension of wedges
zbMATH Keywords: CR-extension
zbMATH Keywords: propagation of CR-extension
author: Burglind Jöricke
reviewed by: Eugen Pascu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921623
OpenAlex ID: W2006968958
description: scientific article; zbMATH DE number 1191284