##### Department of Mathematics,

University of California San Diego

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### PhD Defense

## Gongping Niu

#### UCSD

## Singular Isoperimetric Regions and Twisted Jacobi fields on Locally Stable CMC Hypersurfaces with Isolated Singularities

##### Abstract:

In this talk, we will demonstrate that the well-known singularity Hausdorff dimension estimates for isoperimetric regions are sharp by constructing singular examples in dimensions 8 and higher. Then, to explore the isoperimetric regions under generic Riemannian metrics, we will discuss the twisted Jacobi field of singular constant mean curvature hypersurfaces under certain regularity assumptions.

### May 30, 2024

### 5:00 PM

APM 7321

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