# Plateau's problem for singular curves

## TL;DR

This paper extends the solution of Plateau's problem to singular curves with self-intersections, utilizing a general metric space approach, and presents new results even in Euclidean spaces.

## Contribution

It provides a novel solution to Plateau's problem for singular, self-intersecting curves in broad metric spaces, including Euclidean spaces.

## Key findings

- Solution applicable to singular curves with self-intersections
- Works in very general metric spaces
- Main results are new even in Euclidean spaces

## 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 $\mathbb{R}^n$.