##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Xin Zhou

#### UCSB

## Multiplicity One Conjecture in Min-max theory

##### Abstract:

I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist infinitely many pairwise non-isometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves.

Host: Lei Ni

### January 16, 2019

### 1:00 PM

### AP&M 5829

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