Abstract
For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\le (n+1)\le 7$, 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.
Citation
Kei Irie. Fernando Marques. André Neves. "Density of minimal hypersurfaces for generic metrics." Ann. of Math. (2) 187 (3) 963 - 972, May 2018. https://doi.org/10.4007/annals.2018.187.3.8
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