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arXiv · 1710.10752

Density of minimal hypersurfaces for generic metrics

Kei Irie·Fernando C. Marques·André Neves
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Abstract

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\leq (n+1)\leq 7$, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces thus proving a conjecture of Yau (1982) for generic metrics.

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Kei Irie, Fernando C. Marques, André Neves. 2017-10-30. Density of minimal hypersurfaces for generic metrics. https://arxiv.org/abs/1710.10752

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