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arXiv · 2205.01047

Minimal hypersurfaces for generic metrics in dimension 8

Yangyang Li·Zhihan Wang
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Abstract

We show that in an $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight.

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Yangyang Li, Zhihan Wang. 2022-05-02. Minimal hypersurfaces for generic metrics in dimension 8. https://arxiv.org/abs/2205.01047

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