TY - JOUR
AU1 - Guang, Qiang
AU2 - Li, Martin Man-chun
AU3 - Zhou, Xin
AB - 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.
TI - Curvature estimates for stable free boundary minimal hypersurfaces
JF - Journal für die reine und angewandte Mathematik
DO - 10.1515/crelle-2018-0008
DA - 2020-02-01
UR - https://www.deepdyve.com/lp/de-gruyter/curvature-estimates-for-stable-free-boundary-minimal-hypersurfaces-gwWNXEHA9o
SP - 245
EP - 264
VL - 2020
IS - 759
DP - DeepDyve
ER -