Plateau's problem for singular curves
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Publication:6172848
DOI10.4310/CAG.2022.V30.N8.A3zbMATH Open1525.53004arXiv1904.12567OpenAlexW2941689939MaRDI QIDQ6172848
Publication date: 20 July 2023
Published in: Communications in Analysis and Geometry (Search for Journal in Brave)
Abstract: 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 very general metric spaces by Alexander Lytchak and Stefan Wenger and hence works also in a quite general setting. However the main result of this paper seems to be new even in .
Full work available at URL: https://arxiv.org/abs/1904.12567
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Curves in Euclidean and related spaces (53A04) Singularities of curves, local rings (14H20) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)
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