Freely quasiconformal maps and distance ratio metric - UTU Research Portal

A1 Refereed original research article in a scientific journal

Freely quasiconformal maps and distance ratio metric

Authors: Li Y., Ponnusamy S., Vuorinen M.

Publisher: Cambridge University Press

Publication year: 2014

Journal: Journal of the Australian Mathematical Society

Journal name in source: Journal of the Australian Mathematical Society

Volume: 97

Issue: 3

First page : 383

Last page: 390

Number of pages: 8

ISSN: 1446-8107

DOI: https://doi.org/10.1017/S1446788714000329

Web address : http://api.elsevier.com/content/abstract/scopus_id:84911912997

Abstract

Suppose that (Formula presented.) and (Formula presented.) denote real Banach spaces with dimension at least 2 and that (Formula presented.) and (Formula presented.) are domains. Let (Formula presented.) be a homeomorphism with (Formula presented.). We say that a homeomorphism (Formula presented.) is (Formula presented.)-FQC if for every subdomain (Formula presented.), we have (Formula presented.) holds for all (Formula presented.). In this paper, we establish, in terms of the (Formula presented.) metric, a necessary and sufficient condition for a homeomorphism (Formula presented.) to be FQC. Moreover, we give, in terms of the (Formula presented.) metric, a sufficient condition for a homeomorphism (Formula presented.) to be FQC. On the other hand, we show that this condition is not necessary.