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arxiv: 1811.06913 · v2 · pith:R45ISTX6new · submitted 2018-11-16 · 🧮 math.DG · gr-qc

The mass of an asymptotically hyperbolic manifold with a noncompact boundary

classification 🧮 math.DG gr-qc
keywords boundaryhyperbolicasymptoticallyhalf-spacemanifoldmassnoncompactapplication
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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.

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