On quasisymmetry of quasiconformal mappings

摘要

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.