Regularity of free boundary minimal surfaces in locally polyhedral domains
Differential Geometry
2021-05-27 v2 Analysis of PDEs
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 graphical over this plane. We apply our theorem to prove partial regularity results for free-boundary minimizing hypersurfaces, and relative isoperimetric regions.
Keywords
Cite
@article{arxiv.2006.15441,
title = {Regularity of free boundary minimal surfaces in locally polyhedral domains},
author = {Nicholas Edelen and Chao Li},
journal= {arXiv preprint arXiv:2006.15441},
year = {2021}
}
Comments
Final version, accepted by Comm. Pure. Appl. Math