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The Plateau-Douglas problem for singular configurations and in general metric spaces

Autor: Paul Creutz, Martin Fitzi

Publikováno v: Archive for Rational Mechanics and Analysis

Assume you are given a finite configuration $\Gamma$ of disjoint rectifiable Jordan curves in $\mathbb{R}^n$. The Plateau-Douglas problem asks whether there exists a minimizer of area among all compact surfaces of genus at most $p$ which span $\Gamma

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https://hdl.handle.net/21.11116/0000-000D-041C-021.11116/0000-000D-041E-E21.11116/0000-000D-041F-D

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Majorization by hemispheres and quadratic isoperimetric constants

Autor: Paul Creutz

Publikováno v: Transactions of the American Mathematical Society. 373:1577-1596

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https://doi.org/10.1090/tran/7827

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Space of minimal discs and its compactification

Autor: Paul Creutz

We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the boundary circle. We show that the closure of this class as a subset of Gromov-Hausdorff space is intimat

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Maximal metric surfaces and the Sobolev-to-Lipschitz property

Autor: Paul Creutz, Elefterios Soultanis

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also app

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