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arXiv · 2006.15441

Regularity of free boundary minimal surfaces in locally polyhedral domains

Nicholas Edelen·Chao Li
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Abstract

We prove an Allard-type regularity theorem for free-boundary minimal surfaces in Lipschitz domains locally modelled on convex polyhedra. We show that if such a minimal surface is sufficiently close to an appropriate free-boundary plane, then the surface is $C^{1,\alpha}$ graphical over this plane. We apply our theorem to prove partial regularity results for free-boundary minimizing hypersurfaces, and relative isoperimetric regions.

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Nicholas Edelen, Chao Li. 2020-06-27. Regularity of free boundary minimal surfaces in locally polyhedral domains. https://arxiv.org/abs/2006.15441

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