##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Tom Ilmanen

#### ETH Zurich

## Initial Time Singularities in Mean Curvature Flow

##### Abstract:

\indent Let $M_0$ be a closed subset of $R^n+1$ that is a smooth hypersurface except for a finite number of isolated singular points. Suppose that $M_0$ is asymptotic to a regular cone near each singular point.
Can we flow $M_0$ by mean curvature?
Theorem $(n<7)$: there exists a smooth mean curvature evolution starting at $M_0$ and defined for a short time $0

Host: Lei Ni

### January 26, 2011

### 3:00 PM

### AP&M 5829

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