A regularity and compactness theory for immersed stable minimal hypersurfaces of multiplicity at most 2

Neshan Wickramasekera Massachusetts Institute of Technology University of California

Differential Geometry mathscidoc:1609.10079

Journal of Differential Geometry, 80, (1), 79-173, 2008
We prove that a stable minimal hypersurface of an open ball which is immersed away from a closed (singular) set of finite codimension 2 Hausdorff measure and weakly close to a multiplicity 2 hyperplane must in the interior be the graph over the hyperplane of a 2-valued function satisfying a local C1, estimate. This regularity is optimal under our hypotheses. As a consequence, we also establish compactness of the class of stable minimal hypersur- faces of an open ball which have volume density ratios uniformly bounded by 3−δ for any fixed δ ∈ (0, 1) and interior singular sets of vanishing co-dimension 2 Hausdorff measure.
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@inproceedings{neshan2008a,
  title={A REGULARITY AND COMPACTNESS THEORY FOR IMMERSED STABLE MINIMAL HYPERSURFACES OF MULTIPLICITY AT MOST 2},
  author={Neshan Wickramasekera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909135034413674736},
  booktitle={Journal of Differential Geometry},
  volume={80},
  number={1},
  pages={79-173},
  year={2008},
}
Neshan Wickramasekera. A REGULARITY AND COMPACTNESS THEORY FOR IMMERSED STABLE MINIMAL HYPERSURFACES OF MULTIPLICITY AT MOST 2. 2008. Vol. 80. In Journal of Differential Geometry. pp.79-173. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909135034413674736.
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