##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Brett Kotschwar

#### MIT

## Backwards-uniqueness for the Ricci flow

##### Abstract:

I will discuss the problem of backwards-uniqueness or "unique-continuation" for the Ricci flow, and prove that two complete solutions $g(t)$, $\tilde{g}(t)$ to the Ricci flow on $[0, T]$ of uniformly bounded curvature that agree at $t=T$ must agree identically on $[0, T]$. A consequence is that the isometry group of a solution to the Ricci flow cannot expand in finite time.

Host: Ben Weinkove

### May 14, 2009

### 3:00 PM

### AP&M 6402

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