On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds

TL;DR

This paper proves positive energy theorems for asymptotically hyperbolic manifolds in dimensions 3 to 7, extending previous results through deformation-of-mass-aspect theorems and additional conditions.

Contribution

It introduces deformation-of-mass-aspect theorems for dimensions n≥4 and extends positivity results to n=3 with stricter conditions.

Findings

Positivity of energy established for dimensions 4 to 7.

Extension of positivity results to dimension 3 under stricter conditions.

Development of deformation-of-mass-aspect theorems for higher dimensions.

Abstract

We prove positivity of energy for a class of asymptotically locally hyperbolic manifolds in dimensions $4\le n \le 7$. The result is established by first proving deformation-of-mass-aspect theorems in dimensions $n\ge 4$. Our positivity results extend to the case $n = 3$ when more stringent conditions are imposed.