Topology Seminar (Main Talk): Denseness of minimal hypersurfaces for $C^\infty $-generic metrics

Seminar | February 7 | 2-3 p.m. | 740 Evans Hall

 Kei Irie, Kyoto

 Department of Mathematics

I will explain the following result, which was proved in a paper by Marques-Neves-speaker: on a closed manifold of dimension $3 \le d \le 7$ with a $C^\infty $-generic Riemannian metric, the union of closed, embedded minimal hypersurfaces is dense.

The key ingredient of the proof is an asymptotic formula (Weyl law) of the volume spectrum, which was conjectured by Gromov and proved by Liokumovich-Marques-Neves.