Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 178732, 19 pages
doi:10.1155/2010/178732
Research Article

On Harmonic Quasiconformal Quasi-Isometries

M. Mateljević1 and M. Vuorinen2

1Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia
2Department of Mathematics, University of Turku, 20014, Finland

Received 3 January 2010; Revised 26 March 2010; Accepted 29 March 2010

Academic Editor: Shusen Ding

Copyright © 2010 M. Mateljević and M. Vuorinen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to explore conditions which guarantee Lipschitz-continuity of harmonic maps with respect to quasihyperbolic metrics. For instance, we prove that harmonic quasiconformal maps are Lipschitz with respect to quasihyperbolic metrics.