##### Department of Mathematics,

University of California San Diego

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### Differential Geometry

## Brett Kotschwar

#### ASU

## Time-analyticity of solutions to the Ricci flow

##### Abstract:

We will show that smooth complete solutions to the Ricci flow of uniformly bounded curvature are analytic in time in the interior of their interval of existence. The analyticity is a consequence of classical Bernstein-Bando-Shi type estimates on the temporal and spatial derivatives of the curvature tensor, and offers an alternative proof of the unique continuation of solutions to the Ricci flow. As a further application of these estimates, we will show that, under the above global hypotheses, about any interior space-time point (x0, t0), there exist local coordinates x on a neighborhood U of x0 in which the representation of the metric is real-analytic in both x and t on some cylinder over U.

Host: Ben Chow

### November 8, 2012

### 9:00 AM

### AP&M 7218

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