##### Department of Mathematics,

University of California San Diego

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### Special Geometry

## Pengzi Miao

#### Stanford University

## Mass, quasi-local mass and static metric extension in general relativity

##### Abstract:

We will first discuss a generalized Positive Mass Theorem on a class ofpiecewise smooth asymptotically flat manifolds with broken mean curvatureacross a hypersurface. Then we will relate it to Bartnik's quasi-localmass definition and explain how Corvino's scalar curvaturedeformation theorem implies that a minimal mass extension, if exists,must be static. Finally, we will prove that, for any metric thatis close enough to the Euclidean metric on a ball and has reflectioninvariant boundary data, there always exists an asymptotically flat, scalar flat and static metric extension with Bartnik's geometric boundarycondition.

Host: Kate Okikiolu

### February 18, 2003

### 8:00 AM

### AP&M 7321

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