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.

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.