Density of minimal hypersurfaces for generic metrics

Kei Irie; Fernando C. Marques; André Neves

doi:https://doi.org/10.4007/annals.2018.187.3.8

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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Density of minimal hypersurfaces for generic metrics

Abstract

Authors