Geometric Analysis and Topology Seminar

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Mappings of finite distortion on metric surfaces

Speaker: Damaris Meier, Fribourg

Location: Warren Weaver Hall 512

Date: Friday, April 12, 2024, 11 a.m.

Synopsis:

 Abstract:  Mappings of finite distortion are non-homeomorphic generalizations of quasiconformal maps and originally arose from the study of nonlinear elasticity theory in the 1980s. Ever since, a rich theory has been developed within the Euclidean framework. In recent years, there has been a growing interest in expanding this theory to a non-smooth setting.

In this talk, we introduce a novel approach on studying the distortion of mappings between metric spaces. We show that every non-constant map from a metric surface to the Euclidean plane with locally integrable distortion is continuous, open and discrete; the basic topological properties of complex analytic functions. This generalizes a Euclidean result from Iwaniec-Sverak. Here, a metric surface is a metric space homeomorphic to a planar domain and of locally finite area. Furthermore, we will investigate how this new definition relates to other notions of distortion. Based on joint work with Kai Rajala.