##### Department of Mathematics,

University of California San Diego

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### Postdoc Seminar

## Gongping Niu

#### UCSD

## The existence of singular isoperimetric hypersurfaces

##### Abstract:

It is well-known that isoperimetric hypersurfaces in a smooth, compact (n+1)-manifold are smooth up to a closed set of codimension at least 7. We prove that the dimension estimate of singularities is sharp. In this talk, we will explore an example of an 8-dimensional closed smooth Riemannian manifold, whose unique isoperimetric region, with half the volume of the manifold, displays two isolated singularities on its boundary. Furthermore, for n > 7, we utilize similar methods to construct singular isoperimetric hypersurfaces in higher dimensions.

### November 30, 2023

### 3:00 PM

APM 5829

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