# On the total mass of asymptotically hyperbolic manifolds

## TL;DR

This paper provides an elementary proof of the positivity of hyperbolic mass for asymptotically hyperbolic manifolds, extending Bartnik's Euclidean results to hyperbolic space.

## Contribution

It generalizes Bartnik's positivity proof from Euclidean to hyperbolic manifolds with a new elementary approach.

## Key findings

- Hyperbolic mass is positive near hyperbolic space.
- The proof is elementary and parallels Bartnik's Euclidean case.
- The work extends positivity results to asymptotically hyperbolic manifolds.

## Abstract

Generalising a proof by Bartnik in the asymptotically Euclidean case, we give an elementary proof of positivity of the hyperbolic mass near the hyperbolic space. It is a pleasure to dedicate this work to Robert Bartnik on the occasion of his 60th birthday.

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Source: https://tomesphere.com/paper/1812.03924