Thursday 25 May 2023, 16:00 - 17:00 in HG00.065
Anna Sakovich (Uppsala)
Mass and its positivity in Riemannian Geometry and General Relativity
Suppose that we are given two Riemannian manifolds that 'look alike' near infinity. Under which minimal geometric assumptions can we determine if these two manifolds are identical or different? If one of the two manifolds is either Euclidean space or hyperbolic space, the answer to this question can be provided by an invariant called mass, which was first discovered in General Relativity. In this talk we will discuss geometry and physics behind this rather unique invariant and review some geometric inequalities where it appears. We will conclude by giving a brief outline of our recent proof of the positive mass theorem in the case when the geometry at infinity is asymptotically hyperbolic.