9/21/2007

Andre Neves
Princeton University

Geometry of asymptotically hyperbolic manifolds

I will talk about two topics concerning asymptotically hyperbolic manifolds. The first one concerns the existence and uniqueness of stable spheres with constant mean curvature when the mass of the manifold is positive. This result is obviously false for standard hyperbolic space and so I will explain how the positivity of the mass is used to prove uniqueness. The second topic concerns the Penrose inequality for these manifolds. I will show that  such an inequality holds implies  a nontrivial inequality for functions in S2.   This is joint work with Prof. Tian.