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arxiv: 1801.03442 · v3 · submitted 2018-01-10 · 🌀 gr-qc · math.DG

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

Piotr T. Chru\'sciel , Gregory J. Galloway , Luc Nguyen , Tim-Torben Paetz
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classification 🌀 gr-qc math.DG
keywords asymptoticallydimensionsenergyhyperbolicmanifoldspositivitytheoremsaspect
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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.

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Cited by 1 Pith paper

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  1. Positive mass theorem for initial data sets with arbitrary ends

    math.DG 2026-04 unverdicted novelty 6.0

    The positive mass theorem holds for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition, including those with arbitrary ends.