A holographic principle for the existence of imaginary Killing spinors

Abstract

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.

in Journal of Geometry and Physics, Elsevier, 2015

References in corpus (2)

• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature
• A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type

Cited by in corpus (1)

• On the limiting behavior of the Brown-York quasi-local mass in asymptotically hyperbolic manifolds