English

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