Weakly pseudoconvex domains with non-compact automorphism groups
type: Item
instance of: scholarly article
title: Weakly pseudoconvex domains with non-compact automorphism groups
zbMATH Open document ID: 0617.32030
DOI: 10.1007/BF01456333
author: Steven R. Bell
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164371
review text: The main theorem of this paper is that if \(F_ i: \Omega _ 1\to \Omega _ 2\) is a sequence of biholomorphic mappings between weakly pseudoconvex domains in \({\mathbb{C}}^ n\) with real analytic boundaries such that \(F_ i\) converges uniformly on compact subsets of \(\Omega _ 1\) to a mapping F, then there is a domain D which contains \(\Omega _ 1\) together with all the strictly pseudoconvex boundary points of \(\Omega _ 1\) with the following property: the mappings \(F_ i\) and the mapping F extend holomorphically to D. Furthermore, \(F_ i\) converges uniformly on compact subsets of D to F. The mapping F is either a constant map of \(\Omega _ 1\) into the set of weakly pseudoconvex boundary points of \(\Omega _ 2\), or F is a biholomorphic map. This theorem is a first step toward proving that the class of weakly pseudoconvex domains with non- compact automorphism groups must be small.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 4000371
zbMATH Keywords: biholomorphic mappings between weakly pseudoconvex domains
zbMATH Keywords: non-compact automorphism groups
zbMATH Keywords: holomorphic continuation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4000371