Resonances for Symmetric Tensors on Asymptotically Hyperbolic Spaces

TL;DR

This paper investigates the meromorphic continuation of the resolvent of the Lichnerowicz Laplacian on asymptotically hyperbolic spaces, revealing quantum resonances for symmetric tensors of various ranks.

Contribution

It extends the analysis of resolvent meromorphic continuation and quantum resonances to symmetric tensors on asymptotically hyperbolic manifolds and their quotients.

Findings

Resonances are shown to exist for trace-free, divergence-free symmetric 2-tensors.

Meromorphic continuation of the resolvent is established for higher rank symmetric tensors.

Results apply to manifolds with conformally compact Einstein metrics and hyperbolic quotients.

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.