On quasisymmetry of quasiconformal mappings

M. Huang, S. Ponnusamy, Antti Rasila, Xiantao Wang*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

Suppose that f: D -> D' is a quasiconformal mapping, where D and D' are domains in R-n, and that D is a broad domain. We show that for every arcwise connected subset A in D, the weak quasisymmetry of the restriction f vertical bar A:A -> f(A) implies its quasisymmetry. As a consequence, we see that the answer to one of the open problems raised by Heinonen from 1989 is affirmative, under the additional condition that A is arcwise connected. (C) 2015 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1069-1096
Number of pages28
JournalADVANCES IN MATHEMATICS
Volume288
DOIs
Publication statusPublished - 22 Jan 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Broad domain
  • LLC2 set
  • Quasiconformal mapping
  • Quasisymmetry
  • Weak quasisymmetry
  • LOEWNER SPACES
  • QUASICONFORMALITY
  • DOMAINS
  • HOMEOMORPHISMS
  • MAPS

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