Topics in the Theory of Quasiregular Mappings

Abstract

The theory of quasiregular maps has turned out to form the right generalization of the geometric part of the theory of one complex variable analytic functions to real n-dimen-sional space. These maps can be described as quasiconformal maps witout the homeomorphism requirement and, consequently, they have in general branching. The most interesting geometric features of the theory of quasiregular maps are in general of global character. While many relatively strong and precise results of this nature exist, the connections to differential geometry for example are not well understood and there is much left for further research.