##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Taiyuan Gao

#### JiangSu Norm. University

## Nonlocal curvature flows of closed curves in the plane

##### Abstract:

We first talk about Gage's area-preserving flow (GAPF) for simple, smooth and star-shaped curves. It is shown that GAPF drives a centrosymmetric initial curve into a circle as time tends to infinity. Then we generalize GAPF to deform one convex curve to another. This work gives a partial answer to Yau's problem on realizing Whitney-Graustein Theorem via curvature flows.

Lei Ni

### February 19, 2020

### 10:00 AM

### AP&M 6402

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