Resonances for symmetric tensors on asymptotically hyperbolic spaces

Hadfield, Charles

doi:10.2140/apde.2017.10.1877

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Resonances for symmetric tensors on asymptotically hyperbolic spaces

Charles Hadfield

Vol. 10 (2017), No. 8, 1877–1922

DOI: 10.2140/apde.2017.10.1877

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.

Keywords

quantum resonances, asymptotically hyperbolic, meromorphic extension of resolvent

Mathematical Subject Classification 2010

Primary: 35P25

Secondary: 35Q75, 53B21

Milestones

Received: 24 October 2016

Accepted: 12 July 2017

Published: 18 August 2017

Authors

Charles Hadfield
DMA École Normale Supérieure Paris France

Vol. 10, No. 8, 2017