  Suppose that $\Sigma=\partial\Omega$ is the $n$-dimensional boundary, with
positive (inward) mean curvature $H$, of a connected compact
$(n+1)$-dimensional Riemannian spin manifold $(\Omega^{n+1},g)$ whose scalar
curvature $R\ge -n(n+1)k^2$, for some $k\textgreater{}0$. If $\Sigma$ admits an
isometric and isospin immersion $F$ into the hyperbolic space
${\mathbb{H}^{n+1}\_{-k^2}}$, we define a quasi-local mass and prove its
positivity as well as the associated rigidity statement. The proof is based on
a holographic principle for the existence of an imaginary Killing spinor. For
$n=2$, we also show that its limit, for coordinate spheres in an Asymptotically
Hyperbolic (AH) manifold, is the mass of the (AH) manifold.
