On mean quasiconformal mappings
type: Item
instance of: scholarly article
title: On mean quasiconformal mappings
zbMATH Open document ID: 0877.30009
DOI: 10.1007/BF02104876
published in: Siberian Mathematical Journal
publication date: 1997-06-18T00:00:00Z
review text: Let \(H^\Phi\) be the set of all orientation preserving homeomorphisms \(f:\overline{C}\to \overline{C}\) of the Sobolev space \(W_{1,\text{loc}}^1\) with the normalization \(f(0)=0\), \(f(1)=1\) and \(f(\infty)=\infty\) and the integral condition on the dilatation \(p(z)\) \[ \iint_C \Phi(p(z))dx dy\leq 1. \] The author proves a necessary and sufficient compactness result and a compactification result for the set \(H^\Phi\) in the case of a function \(\Phi\) with exponential growth.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 1023970
zbMATH Keywords: compactness
author: Vladimir I. Ryazanov
reviewed by: Bodo Dittmar
MaRDI profile type: Publication
cites work: On quasiconformal mappings
cites work: Q5617821
cites work: Solutions de l'equation de Beltrami avec ||\mu||_\infty = 1
cites work: Compactness properties of μ-homeomorphisms
cites work: Some questions of convergence and compactness for quasiconformal mappings
cites work: Q3483529
cites work: Q3362186
cites work: Q3262940
cites work: Q5563548
cites work: Q4157538
cites work: Q5335321
cites work: Q5527180
full work available at URL: https://doi.org/10.1007/bf02104876
OpenAlex ID: W1980258772
description: scientific article; zbMATH DE number 1023970