##### Department of Mathematics,

University of California San Diego

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### Informal Differential Geometry Seminar

## Shijin Zhang

#### UCSD

## Ricci flow coupled with harmonic map flow --- Reto Muller's work

##### Abstract:

Reto Muller investigated a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $\phi$ from $M$ to some closed target closed manifold $N$, given by $\frac{\partial}{\partial t} g = - 2 Ric + 2 \alpha \nabla \phi \bigotimes \nabla \phi, \frac{\partial}{\partial t}\phi = \tau_{g}\phi $, where $\alpha$ is a positive coupling constant. This new flow shares many good properties with the Ricci flow.

### October 29, 2009

### 10:30 AM

### AP&M 5402

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