The radial behavior of a quasiconformal mapping
type: Item
instance of: scholarly article
title: The radial behavior of a quasiconformal mapping
zbMATH Open document ID: 0834.30022
DOI: 10.1215/S0012-7094-94-07424-3
author: Pekka Koskela
published in: Duke Mathematical Journal
publication date: 1994-08-25T00:00:00Z
review text: The author proves three interesting theorems for quasiconformal maps in \(\mathbb{R}^n\), \(n\geq 2\). We state the first result here. Theorem: Let \(f\) be a \(K\)-quasiconformal mapping of \(B^n\) into \(\mathbb{R}^n\). Then for each \(0< \lambda\leq n- 1\) there exists a set of zero \(\lambda\)- dimensional Hausdorff measure on \(S^{n- 1}= \partial B^n\) such that the Hausdorff dimension of the image of \(S^{n- 1}\backslash E\) ist at most \(\lambda'\), where \(\lambda'< n\) depends only on the dilatation \(K\) of \(f\), \(\lambda\), and \(n\). In particular, there is a set \(F\subset S^{n- 1}\) of Hausdorff dimension zero such that the volume of \(f(S^{n -1}\backslash F)\) is zero.
reviewed by: M. Vuorinen
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 624967
zbMATH Keywords: distortion theorem
zbMATH Keywords: quasiconformal maps
MaRDI profile type: Publication
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full work available at URL: s0012-7094-94-07424-3
OpenAlex ID: W2095388141
description: scientific article; zbMATH DE number 624967