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

Neshan Wickramasekera

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

Differential Geometry 2007-10-10 v1

Authors: Neshan Wickramasekera

Abstract

We prove that a stable minimal hypersurface of an open ball having a singular set of locally finite codimension 2 Hausdorff measure which is weakly close to a multiplicity 2 hyperplane is a 2-valued C^{1, alpha} graph in the interior. Applications including a compactness theorem for a class of immersed stable minimal hypersurfaces and a pointwise curvature estimate for the hypersurfaces in this class in low dimensions are also discussed.

Keywords

stable minimal hypersurfaces regularity theory compactness theorem multiplicity 2 singular set hausdorff measure curvature estimate

Cite

@article{arxiv.0710.1740,
  title  = {A regularity and compactness theory for immersed stable minimal hypersurfaces of multiplicity at most 2},
  author = {Neshan Wickramasekera},
  journal= {arXiv preprint arXiv:0710.1740},
  year   = {2007}
}

Comments

77 pages; to appear in JDG

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