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

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

2007-10-09

arxiv.org/abs/0710.1740v1

Mathematics

Differential Geometry

77 pages; to appear in JDG

Scientific paper

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.

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