Curvature estimates for stable free boundary minimal hypersurfaces
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AbstractIn this paper, we prove uniform curvature estimates for immersed stable free boundary minimal hypersurfaces satisfying a uniform area bound, which generalize the celebrated Schoen–Simon–Yau interior curvature estimates up to the free boundary. Our curvature estimates imply a smooth compactness theorem which is an essential ingredient in the min-max theory of free boundary minimal hypersurfaces developed by the last two authors. We also prove a monotonicity formula for free boundary minimal submanifolds in Riemannian manifolds for any dimension and codimension. For 3-manifolds with boundary, we prove a stronger curvature estimate for properly embedded stable free boundary minimal surfaces without a-priori area bound. This generalizes Schoen’s interior curvature estimates to the free boundary setting. Our proof uses the theory of minimal laminations developed by Colding and Minicozzi.
All Author(s) ListQiang Guang, Martin Man-chun Li, Xin Zhou
Journal nameJournal für die reine und angewandte Mathematik
Volume Number759
Pages245 - 264
LanguagesEnglish-United States
Keywordsminimal surfaces, free boundary problems, curvature estimates

Last updated on 2020-27-03 at 04:37