Branched folded maps and alternating Beltrami equations
type: Item
instance of: scholarly article
title: Branched folded maps and alternating Beltrami equations
zbMATH Open document ID: 0876.30018
DOI: 10.1007/BF02820441
author: U Srebro
author: E. Yakubov
published in: Journal d'Analyse Mathématique
publication date: 1997-11-11T00:00:00Z
review text: The paper under review deals with the Beltrami equation \(w_{\overline z}(z)=\mu(z)w_z(z)\) in a plane domain \(D\) of \(C\). In the classical case \(|\mu|_\infty<1\) an existence and representation theorem is well-known. The authors consider the so-called relaxed classical case \(|\mu|<1\) a.e., \(|\mu|_\infty=1\) and the so-called alternating case \(|\mu|<1\) in parts of \(D\) and \(|\mu|>1\) in other parts of \(D\). In the relaxed classical case sufficient conditions for existence and uniqueness of \(\mu\)-homeomorphisms are given. In order to study the alternating case the authors use, the so-called branched folded maps (BF-maps) (see for instance: \textit{V. I. Arnol'd} [Singularities of caustics and wave fronts (1990; Zbl 0734.53001)]). The local behavior of a BF-map in isolated critical points is considered. For the alternating case a kind of counter part of the classical uniqueness and representation theorem is proved.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 1019375
reviewed by: Bodo Dittmar
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02820441
OpenAlex ID: W2079449696
description: scientific article; zbMATH DE number 1019375