##### Department of Mathematics,

University of California San Diego

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### Joint UCI and UCSD Geometry Seminar

## Ben Weinkove

#### Harvard University

## The Calabi-Yau equation and symplectic geometry

##### Abstract:

The Riemannian Penrose inequality in dimensions less than 8 Abstract: The Positive Mass Theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass. The Riemannian Penrose inequality provides a sharp lower bound for the mass when black holes are present. More precisely, this lower bound is given in terms of the area of an outermost minimal surface, and equality is achieved only for Schwarzschild metrics. The Riemannian Penrose inequality was first proved in three dimensions in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole. In 1999, H. Bray extended this result to the general case of multiple black holes using a different technique. In this talk we extend Bray's technique to dimensions less that 8. This is joint work with H. Bray.

Host: Lei Ni

### June 5, 2007

### 3:00 PM

### AP&M 6402

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