##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Paul Bryan

#### UCSD

## Isoperimetric comparison techniques for Ricci flow on surfaces

##### Abstract:

In this talk I shall present an isoperimetric comparison theorem for the Ricci flow on surfaces, inspired by Hamilton's isoperimetric estimate. I will show how this can be used to prove the Hamilton/Chow theorem, that the Ricci flow converges to a constant curvature metric, thus for example providing a proof of the famous uniformization theorem. This was joint work with Ben Andrews.

### October 25, 2012

### 10:00 AM

### AP&M 7218

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