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Regularity of free boundary minimal surfaces in locally polyhedral domains (2006.15441v2)
Published 27 Jun 2020 in math.DG and math.AP
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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