Seminar

We discuss various definitions for Quasiregular mappings in metric measure spaces. Quasiregular maps, or mappings of bounded distortion, are defined as non-homeomorphic quasiconformal mappings, much like analytic functions in the complex plane can be defined as non-homeomorphic conformal mappings. Quasiregular mappings in Euclidean space were introduced by Reshetyak in the late 60’s, and were later generalized to Carnot groups by Vodop’yanov. Very recently, there have been further generalizations; Onninen and Rajala studied quasiregular mappings from Euclidean space into certain cohomology manifolds, while Cristea considered a broad class of metric spaces. I will discuss a number of results showing new equivalences between different definitions, providing a somewhat more complete picture of the latter setting.