Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains

Nick Edelen, Chao Li

Research output: Contribution to journalArticlepeer-review


We prove an Allard-type regularity theorem for free-boundary minimal surfaces in Lipschitz domains locally modeled on convex polyhedra. We show that if such a minimal surface is sufficiently close to an appropriate free-boundary plane, then the surface is (Formula presented.) graphical over this plane. We apply our theorem to prove partial regularity results for free-boundary minimizing hypersurfaces, and relative isoperimetric regions.

Original languageEnglish (US)
Pages (from-to)970-1031
Number of pages62
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - May 2022

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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