Abstract: In this talk, we introduce a novel approach on studying the distortion of not necessarily homeomorphic 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 Hausdorff 2-measure. Furthermore, we will investigate how this new definition relates to other notions of distortion and formulate open questions. Based on joint work with Kai Rajala.
