# Mass rigidity for hyperbolic manifolds

## TL;DR

This paper proves a mass rigidity theorem for asymptotically hyperbolic manifolds, establishing that equality in the positive mass theorem implies the manifold is hyperbolic space, extending previous results to more general cases.

## Contribution

It generalizes the positive mass theorem rigidity result to non-spin asymptotically hyperbolic manifolds without special asymptotics.

## Key findings

- Mass equality implies the manifold is hyperbolic space
- Extends rigidity results beyond spin manifolds
- No special asymptotics required

## Abstract

We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds or under special asymptotics.