The mass of an asymptotically hyperbolic manifold with a noncompact boundary
Differential Geometry
2019-01-04 v2 General Relativity and Quantum Cosmology
Abstract
We define a mass-type invariant for asymptotically hyperbolic manifolds with a noncompact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable dominant energy conditions. As an application we show that any such manifold which is Einstein and either has a totally geodesic boundary or is conformally compact and has a mean convex boundary is isometric to the hyperbolic half-space.
Keywords
Cite
@article{arxiv.1811.06913,
title = {The mass of an asymptotically hyperbolic manifold with a noncompact boundary},
author = {Sergio Almaraz and Levi Lopes de Lima},
journal= {arXiv preprint arXiv:1811.06913},
year = {2019}
}
Comments
24 pages; no figures; minor modifications in the text to improve the presentation