Plateau’s problem for singular curves

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 $\mathbb{R}^n$.

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The author was partially supported by the DFG grant SPP 2026.

Received 17 May 2019

Accepted 11 March 2020

Published 13 July 2023