D. Meier

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math.MG2026

Monotone Sobolev extensions in metric surfaces and applications to uniformization

Damaris Meier, Noa Vikman, Stefan Wenger

We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to pr…

math.MG2024

Mappings of finite distortion on metric surfaces

Damaris Meier, Kai Rajala

We investigate basic properties of mappings of finite distortion $f : X \to R^{2}$ , where $X$ is any metric surface, i.e., metric space homeomorphic to a planar domain with lo…

math.MG2024

Definitions of quasiconformality on metric surfaces

Damaris Meier, Kai Rajala

We explore the interplay between different definitions of distortion for mappings $f : X \to R^{2}$ , where $X$ is any metric surface, meaning that $X$ is homeomorphic to…