5 citations · 7 across the 9 of their papers we have counts for
9 papers
Length distortion of volume-preserving Lipschitz mappings
Damaris Meier, Kai Rajala
We show that every area-preserving Lipschitz map between metric surfaces distorts the length of almost every curve by at most a multiplicative factor, answering a question posed by…
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…
Energy minimizing harmonic 2-spheres in metric spaces
Damaris Meier, Noa Vikman, Stefan Wenger
In their seminal 1981 article, Sacks-Uhlenbeck famously proved the existence of non-trivial harmonic 2-spheres in every closed Riemannian manifold with non-zero second homotopy gro…
Definitions of quasiconformality on metric surfaces
Damaris Meier, Kai Rajala
We explore the interplay between different definitions of distortion for mappings , where is any metric surface, meaning that is homeomorphic to…
Mappings of finite distortion on metric surfaces
Damaris Meier, Kai Rajala
We investigate basic properties of mappings of finite distortion , where is any metric surface, i.e., metric space homeomorphic to a planar domain with lo…
Lipschitz-Volume rigidity and Sobolev coarea inequality for metric surfaces
Damaris Meier, Dimitrios Ntalampekos
We prove that every 1-Lipschitz map from a closed metric surface onto a closed Riemannian surface that has the same area is an isometry. If we replace the target space with a non-s…
Quasiconformal uniformization of metric surfaces of higher topology
Damaris Meier
We establish the following uniformization result for metric spaces of finite Hausdorff 2-measure. If is homeomorphic to a smooth 2-manifold with non-empty boundary, the…
Canonical parametrizations of metric surfaces of higher topology
Martin Fitzi, Damaris Meier
We give an alternate proof to the following generalization of the uniformization theorem by Bonk and Kleiner. Any linearly locally connected and Ahlfors 2-regular closed metric sur…
Quasiconformal almost parametrizations of metric surfaces
Damaris Meier, Stefan Wenger
We look for minimal conditions on a two-dimensional metric surface of locally finite Hausdorff -measure under which admits an (almost) parametrization with good geometri…