Resonances for symmetric tensors on asymptotically hyperbolic spaces

Abstract

On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex plane, defining quantum resonances of this Laplacian. For higher-rank symmetric tensors, a similar result is proven for (convex cocompact) quotients of hyperbolic space.