Almost Rigidity of the Positive Mass Theorem for Asymptotically Hyperbolic Manifolds with Spherical Symmetry

摘要

We use the notion of intrinsic flat distance to address the almost rigidityof the positive mass theorem for asymptotically hyperbolic manifolds. Inparticular, we prove that a sequence of spherically symmetric asymptoticallyhyperbolic manifolds satisfying the conditions of the positive mass theoremconverges to hyperbolic space in the intrinsic flat sense, if the limit of themass along the sequence is zero.