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Generic Regularity of Minimal Hypersurfaces in Dimension 8

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arxiv 2012.05401 v2 pith:TLT4HXDG submitted 2020-12-10 math.DG math.AP

Yangyang Li , Zhihan Wang This is my paper · ORCID
classification math.DGmath.AP
keywords genericminimalperturbationadmitsargumentchodosh-liokumovich-spolaorclosedconstruction
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abstract

In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics admits a smooth minimal hypersurface. This generalized previous results by N. Smale and Chodosh-Liokumovich-Spolaor. Different from their local perturbation techniques, our construction is based on a global perturbation argument in and a novel geometric invariant which counts singular points with suitable weights.

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  1. Non-persistence of strongly isolated singularities, and geometric applications

    math.DG 2024-11 accept novelty 8.0 of 10

    For generic metrics, stationary varifolds with only strongly isolated singularities either are smooth or have a more complicated singularity; in codimension one, only smooth or non-strongly-isolated objects persist.

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