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

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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.

fields

cs.LG 1

years

2023 1

verdicts

UNVERDICTED 1

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