April 2, 2021.
Hyperbolic Mass via Horospheres.
Asymptotically hyperbolic (AH) manifolds arise naturally in general relativity as a spacelike hypersurface in an asymptotically Minkowski spacetime or an asymptotically AdS spacetime. The mass of AH manifolds is a geometric invariant that measures its deviation from hyperbolic space. In this talk, we present a new mass formula using large coordinate horospheres. The formula is stated as a limit of the (weighted) total difference of mean curvatures on large coordinate horospheres. We remark on a few geometric implications of the formula including scalar curvature rigidity of AH manifolds. This talk is based on joint work with Pengzi Miao.