We define a mass-type invariant for asymptotically hyperbolic manifolds with a non-compact 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.

中文翻译：

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具有非紧边界的渐近双曲流形的质量

我们为具有非紧边界的渐近双曲流形定义了一个质量类型不变量，其在双曲半空间上的无穷大处建模，并证明在自旋情况下在合适的主导能量条件下存在尖锐的正质量不等式。作为一个应用，我们表明，任何这样的流形都是爱因斯坦，要么具有完全测地线边界，要么保形紧凑，并且平均凸边界与双曲半空间等距。