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Résonances sur les variétés asymptotiquement hyperboliques

Abstract : We study the meromorphic extension of the resolvent for the Laplacian on a class of non-compact complete Riemannian manifolds whose curvatures approach -1 at infinity. We show that the resolvent extends meromorphically to C with poles of finite multiplicity (called resonances) if and only if the metric satisfies a certain condition of asymptotic evenness, then we construct examples for which there exists a sequence of resonances converging to a point of the non-physical sheet, proving that some essential singularities can appear without this condition. Secondly, we show that the resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for a discrete set of points for which an explicit geometric formula between the multiplicities is given. We finally prove the existence of a free of resonance region exponentially close to the critical line.
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Contributor : Colin Guillarmou <>
Submitted on : Thursday, September 9, 2004 - 9:37:15 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Thursday, September 13, 2012 - 11:50:29 AM


  • HAL Id : tel-00006860, version 1



Colin Guillarmou. Résonances sur les variétés asymptotiquement hyperboliques. Mathématiques [math]. Université de Nantes, 2004. Français. ⟨tel-00006860⟩



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