André NEVES - Gromov’s Weyl Law and Denseness of minimal hypersurfaces
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2017-12-27

Minimal  surfaces  are  ubiquitous  in  Geometry  but  they  are  quite  hard  to  find.
For instance, Yau  in  1982  conjectured  that  any  3-manifold  admits infinitely  many  closed minimal surfaces but the best one knows is the existence of at least two.
In a different direction, Gromov conjectured a Weyl Law for the volume spectrum that was proven last year by Liokumovich, Marques, and myself.
I will cover a bit the history of the problem and then talk about recent work with Irie, 
Marques,  and  myself: we  combined Gromov’s  Weyl  Law  with  the  Min-max  theory Marques  and  I  have  been  developing  over  the  last  years to  prove  that,  for  generic metrics, not only there are infinitely many minimal hypersurfaces but they are also dense.