A holographic principle for the existence of imaginary Killing spinors

Suppose that Σ=∂Ω is the n-dimensional boundary, with positive (inward) mean curvature H, of a connected compact (n+1)-dimensional Riemannian spin manifold (Ωn+1,g) whose scalar curvature R≥−n(n+1)k2, for some k>0. If Σ admits an isometric and isospin immersion F into the hyperbolic space H−k2n+1, 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.