##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Yongjia Zhang

#### UCSD

## On the equivalence between bounded entropy and noncollapsing for ancient solutions to the Ricci flow.

##### Abstract:

At the beginning of section 11 in Perelman's celebrated paper ``The entropy formula for the Ricci flow and its geometric applications'', he made the assertion that for an ancient solution to the Ricci flow with bounded nonnegative curvature operator, bounded entropy is equivalent to noncollapsing on all scales. We give a proof for this assertion.

Host: Lei Ni

### October 17, 2018

### 2:00 PM

### AP&M 5829

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