International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 569481, 13 pages
Research Article

Hyperbolically Bi-Lipschitz Continuity for -Harmonic Quasiconformal Mappings

Department of Mathematics, Huaqiao University, Fujian, Quanzhou 362021, China

Received 25 March 2012; Accepted 23 May 2012

Academic Editor: Oscar Blasco

Copyright © 2012 Xingdi Chen. 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.


We study the class of -harmonic -quasiconformal mappings with angular ranges. After building a differential equation for the hyperbolic metric of an angular range, we obtain the sharp bounds of their hyperbolically partial derivatives, determined by the quasiconformal constant . As an application we get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschitz coefficients.