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math.DG2020
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…
math.DG2019
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…
math.DG2019
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…