Density of minimal hypersurfaces for generic metrics

Kei Irie; Fernando C. Marques; André Neves

Density of minimal hypersurfaces for generic metrics

Differential Geometry 2018-02-12 v2 Analysis of PDEs Geometric Topology

Authors: Kei Irie , Fernando C. Marques , André Neves

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.

Keywords

minimal hypersurfaces generic metrics Riemannian metrics Baire sense density Yau conjecture

Cite

@article{arxiv.1710.10752,
  title  = {Density of minimal hypersurfaces for generic metrics},
  author = {Kei Irie and Fernando C. Marques and André Neves},
  journal= {arXiv preprint arXiv:1710.10752},
  year   = {2018}
}

Comments

Revised version. To appear in Annals of Mathematics

Related papers

View all related →