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arXiv · 2507.13189

Optimal regularity up to the boundary for Plateau-quasi-minimizers

Eve Machefert
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Abstract

We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with Ahlfors regular boundaries. This requires to investigate the Ahlfors regularity and also the uniform rectifiability of those sets, up to the boundary.

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Eve Machefert. 2025-07-17. Optimal regularity up to the boundary for Plateau-quasi-minimizers. https://arxiv.org/abs/2507.13189

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