Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains

  title={Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains},
  author={Nick Edelen and Chaobo Li},
  journal={Communications on Pure and Applied Mathematics},
  • Nick Edelen, Chaobo Li
  • Published 27 June 2020
  • Mathematics
  • Communications on Pure and Applied Mathematics
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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