##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Yuxin Ge

#### University Paris 12 \\ University of Washington

## On the $\sigma_2$-scalar curvature and its application

##### Abstract:

In this talk, we establish an analytic foundation for a fully non-linear equation $\frac{\sigma_2}{\sigma_1}=f$ on manifolds with positive scalar curvature. This equation arises from conformal geometry. As application, we prove that, if a compact 3-dimensional manifold $M$ admits a riemannian metric with positive scalar curvature and $\int \sigma_2\ge 0$, then topologically $M$ is a quotient of sphere.

Hosts: Ben Chow and Lei Ni

### March 10, 2008

### 4:00 PM

### AP&M 6402

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