Wiman and Arima Theorems for Quasiregular Mappings

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.