Quasiconformal concordance
type: Item
instance of: scholarly article
title: Quasiconformal concordance
zbMATH Open document ID: 0685.30010
DOI: 10.1007/BF01300921
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178419
review text: Two maps \(f_ 0,f_ 1: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) are called quasiconformally concordant if there is a quasiconformal homeomorphism F: \({\mathbb{R}}^ n\times I\to {\mathbb{R}}^ n\times I\) such that \(F(x,0)=(f_ 0(x),0)\) and \(F(x,1)=(f_ 1(x),1)\). The main result of the paper gives the following necessary and sufficient condition for the quasiconformal concordance of \(f_ 0\) and \(f_ 1:\) (1) \(f_ 0\) and \(f_ 1\) are quasisymmetric, (2) \(f_ 0\), \(f_ 0^{-1}\), \(f_ 1\), \(f_ 1^{-1}\) are uniformly continuous, (3) \(f_ 0-f_ 1\) is bounded. If \(n\geq 2\), (1) means that \(f_ 0\) and \(f_ 1\) are quasiconformal. A bilipschitz version is also given.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 4122282
author: Jussi Väisälä
MaRDI profile type: Publication
cites work: Q5511142
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OpenAlex ID: W4235998032
description: scientific article; zbMATH DE number 4122282