Ricci Curvature Rigidity for Weakly Asymptotically Hyperbolic Manifolds

Vincent Bonini, Pengzi Miao and Jie Qing

We obtain rigidity results for Riemannian manifolds which are weakly asymptotically hyperbolic and have lower bound on Ricci curvature. Our argument consists of two steps. First we compactify the metric by its positive eigenfunction. Then we apply a quasi-local mass characterization of Euclidean balls to the compactified metric. As a result, a weak asymptotic condition on the metric is obtained to assure the rigidity.