Vol. 10, No. 8, 2017
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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