On quasisymmetry of quasiconformal mappings

M. Huang, S. Ponnusamy, A. Rasila, X. Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Suppose that f:D→D' is a quasiconformal mapping, where D and D' are domains in Rn, 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|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.

Original languageEnglish
Pages (from-to)1069-1096
Number of pages28
JournalAdvances in Mathematics
Volume288
DOIs
StatePublished - 22 Jan 2016

Keywords

  • Broad domain
  • LLC set
  • Quasiconformal mapping
  • Quasisymmetry
  • Weak quasisymmetry

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