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arXiv · 2609.15507

Existence of least-area discs

Alexander Lytchak·Stephan Stadler
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Abstract

We prove that every closed Lipschitz curve in Euclidean space extends to a Lipschitz disc of least area. The proof is geometric and applies more generally to metric spaces with curvature bounded above in the sense of Alexandrov.

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Alexander Lytchak, Stephan Stadler. 2026-09-14. Existence of least-area discs. https://arxiv.org/abs/2609.15507

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