Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds

Abstract

The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result and a positive mass theorem for asymptotically hyperbolic manifolds that do not require a spin assumption. The positive mass theorem is reduced to the rigidity case by a deformation construction near the conformal boundary. The proof of the rigidity result is based on a study of minimizers of the BPS brane action.