Vol. 10, No. 8, 2017

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Resonances for symmetric tensors on asymptotically hyperbolic spaces

Charles Hadfield

Vol. 10 (2017), No. 8, 1877–1922
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