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arXiv · 2012.05401

Generic Regularity of Minimal Hypersurfaces in Dimension 8

Yangyang Li·Zhihan Wang
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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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Yangyang Li, Zhihan Wang. 2020-12-10. Generic Regularity of Minimal Hypersurfaces in Dimension 8. https://arxiv.org/abs/2012.05401

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