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

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.15441
 Bibcode:
 2020arXiv200615441E
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 Final version, accepted by Comm. Pure. Appl. Math