# Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains

@article{Edelen2022RegularityOF, title={Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains}, author={Nick Edelen and Chaobo Li}, journal={Communications on Pure and Applied Mathematics}, year={2022} }

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.

## One Citation

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