Harmonic mappings of multiply connected domains
type: Item
instance of: scholarly article
title: Harmonic mappings of multiply connected domains
zbMATH Open document ID: 0885.30020
author: Peter Duren
author: Walter Hengartner
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
review text: The Radó-Kneser-Choquet theorem is extended in two different ways to multiply connected domains. One is a direct continuation of Kneser's idea and has nothing to do with convexity; while the other asserts that a finitely connected domain can be mapped harmonically with prescribed outer boundary correspondence onto a given convex domain with suitable punctures. It is also shown that a domain containing infinity admits a unique harmonic mapping, with standard normalization at infinity, onto a punctured plane. For domains of connectivity \(n\) the dilatation of the canonical mapping covers the unit disk exactly \(2n\) times. Furthermore, no other normalized harmonic mapping has the same dilatation.
reviewed by: Peter Duren
Mathematics Subject Classification ID: 30C99
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 30C35
zbMATH DE Number: 950188
zbMATH Keywords: Radó-Kneser-Choquet theorem
zbMATH Keywords: multiply connected domains
zbMATH Keywords: connected domain
zbMATH Keywords: convex domain
zbMATH Keywords: harmonic mapping
zbMATH Keywords: domains of connectivity
zbMATH Keywords: dilatation
zbMATH Keywords: canonical mapping
MaRDI profile type: Publication
full work available at URL: pjm.1997.180.201
OpenAlex ID: W2009515573
DOI: 10.2140/PJM.1997.180.201
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description: scientific article; zbMATH DE number 950188