Plateau's problem for singular curves
P Creutz - arXiv preprint arXiv:1904.12567, 2019 - arxiv.org
We give a solution of Plateau's problem for singular curves possibly having self-
intersections. The proof is based on the solution of Plateau's problem for Jordan curves in …
intersections. The proof is based on the solution of Plateau's problem for Jordan curves in …
Maximal metric surfaces and the Sobolev-to-Lipschitz property
P Creutz, E Soultanis - Calculus of Variations and Partial Differential …, 2020 - Springer
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors
regular spheres these are uniquely characterized by satisfying the seemingly unrelated …
regular spheres these are uniquely characterized by satisfying the seemingly unrelated …
Curvature bounds on length-minimizing discs
A Lytchak, S Wagner - Geometriae Dedicata, 2024 - Springer
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The branch set of minimal disks in metric spaces
We study the structure of the branch set of solutions to Plateau's problem in metric spaces
satisfying a quadratic isoperimetric inequality. In our 1st result, we give examples of spaces …
satisfying a quadratic isoperimetric inequality. In our 1st result, we give examples of spaces …
The plateau-douglas problem for singular configurations and in general metric spaces
P Creutz, M Fitzi - Archive for Rational Mechanics and Analysis, 2023 - Springer
Assume you are given a finite configuration Γ of disjoint rectifiable Jordan curves in R n. The
Plateau-Douglas problem asks whether there exists a minimizer of area among all compact …
Plateau-Douglas problem asks whether there exists a minimizer of area among all compact …