4 papers
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…
The Plateau-Douglas problem for singular configurations and in general metric spaces
Paul Creutz, Martin Fitzi
Assume you are given a finite configuration of disjoint rectifiable Jordan curves in . The Plateau-Douglas problem asks whether there exists a minimizer of area a…
Morrey's -conformality lemma in metric spaces
Martin Fitzi, Stefan Wenger
We provide a simpler proof and slight strengthening of Morrey's famous lemma on -conformal mappings. Our result more generally applies to Sobolev maps with values in a…
Area minimizing surfaces of bounded genus in metric spaces
Martin Fitzi, Stefan Wenger
The Plateau-Douglas problem asks to find an area minimizing surface of fixed or bounded genus spanning a given finite collection of Jordan curves in Euclidean space. In the present…