##### Department of Mathematics,

University of California San Diego

****************************

### Math 258 - Differential Geometry Seminar

## Yangyang Li

#### Princeton University

## Generic Regularity of Minimal Hypersurfaces in Dimension 8

##### Abstract:

The well-known Simons's cone suggests that minimal hypersurfaces could be possibly singular in a Riemannian manifold with dimension greater than 7, unlike the lower dimensional case. Nevertheless, it was conjectured that one could perturb away these singularities generically. In this talk, I will discuss how to perturb them away to obtain a smooth minimal hypersurface in an 8-dimension closed manifold, by induction on the ``capacity" of singular sets. This result generalizes the previous works by N. Smale and by Chodosh-Liokumovich-Spolaor to any 8-dimensional closed manifold. \\ \\ This talk is based on joint work with Zhihan Wang.

Hosts: Lei Ni and Luca Spolaor

### April 21, 2021

### 11:00 AM

### Zoom ID 917 6172 6136

****************************