Geodesic
Density of minimal hypersurfaces for generic metrics
Kei Irie1 ; Fernando C. Marques2 ; André Neves3
1 Research Institute for Mathematical Sciences Kyoto University, Kyoto Japan and Simons Center for Geometry and Physics State, University of New York Stony Brook, NY
2 Department of Mathematics, Princeton University, Princeton, NJ
3 Department of Mathematics, University of Chicago, Chicago, IL and Imperial College London, London, UK
Annals of mathematics, Tome 187 (2018) no. 3, pp. 963-972

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2018.187.3.8

Kei Irie 1 ; Fernando C. Marques 2 ; André Neves 3

1 Research Institute for Mathematical Sciences Kyoto University, Kyoto Japan and Simons Center for Geometry and Physics State, University of New York Stony Brook, NY
2 Department of Mathematics, Princeton University, Princeton, NJ
3 Department of Mathematics, University of Chicago, Chicago, IL and Imperial College London, London, UK 
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Kei Irie; Fernando C. Marques; André Neves. Density of minimal hypersurfaces for generic metrics. Annals of mathematics, Tome 187 (2018) no. 3, pp. 963-972. doi: 10.4007/annals.2018.187.3.8

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