Valancy of harmonic mappings onto bounded convex domains
type: Item
instance of: scholarly article
title: Valancy of harmonic mappings onto bounded convex domains
zbMATH Open document ID: 1017.30015
DOI: 10.1007/BF03321003
author: Daoud Bshouty
author: Walter Hengartner
author: Abdallah Lyzzaik
author: Allen Weitsman
published in: Computational Methods and Function Theory
publication date: 2003-01-08T00:00:00Z
review text: The authors show that the Sheil-Small conjecture is false. This conjecture is: if \(f\) is a harmonic mapping of \(\mathbb{D}\) onto a convex Jordan domain \(K\) that extends continuously to \(n\)-valent sense preserving local homeomorphism between \(\partial\mathbb{D}\) and \(\partial K\) and assumes every point in \(\partial K\) exactly \(n\) times, then the valency of \(f\) is at most \(n^2\).
Mathematics Subject Classification ID: 30C55
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 30F99
zbMATH DE Number: 1851121
reviewed by: Dumitru Acu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1851121