Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 604217, 29 pages
doi:10.1155/2010/604217
Research Article

Wiman and Arima Theorems for Quasiregular Mappings

O. Martio,1 V. M. Miklyukov,2 and M. Vuorinen3

1Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland
2Department of Mathematics, Volgograd State University, 2 Prodolnaya 30, Volgograd 400062, Russia
3Department of Mathematics, University of Turku, 20014 Turku, Finland

Received 28 December 2009; Accepted 11 February 2010

Academic Editor: Shusen Ding

Copyright © 2010 O. Martio et al. 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

Wiman's theorem says that an entire holomorphic function of order less than 1/2 has a minimum modulus converging to ∞ along a sequence. Arima's theorem is a refinement of Wiman's theorem. Here we generalize both results to quasiregular mappings in the manifold setup. The so called fundamental frequency has an important role in this study.