Mass Rigidity for Hyperbolic Manifolds

Abstract

We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality p0=p12+⋯+pn2 holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).