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.

39 pages, notational update, to appear in Analysis & PDE

References in corpus (2)

• Power spectrum of the geodesic flow on hyperbolic manifolds
• Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates

Cited by in corpus (3)

• Stability of Minkowski space and polyhomogeneity of the metric
• Fried conjecture in small dimensions
• Asymptotically Euclidean metrics without conjugate points are flat