On quasisymmetry of quasiconformal mappings

Authors

M. Huang, Hunan Normal University
S. Ponnusamy, Indian Statistical Institute Chennai
A. Rasila, Aalto University
X. Wang, Shantou University

Article Type

Research Article

Publication Title

Advances in Mathematics

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.

First Page

1069

Last Page

1096

DOI

10.1016/j.aim.2015.09.036

Publication Date

1-22-2016

Comments

Open Access; Bronze Open Access

Recommended Citation

Huang, M.; Ponnusamy, S.; Rasila, A.; and Wang, X., "On quasisymmetry of quasiconformal mappings" (2016). Journal Articles. 4345.
https://digitalcommons.isical.ac.in/journal-articles/4345