Upper and Lower Bounds on Resonances for Manifolds Hyperbolic Near Infinity |
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Authors: | David Borthwick |
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Institution: | 1. Department of Mathematics and Computer Science , Emory University , Atlanta, Georgia, USA davidb@mathcs.emory.edu |
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Abstract: | For a conformally compact manifold that is hyperbolic near infinity and of dimension n + 1, we complete the proof of the optimal O(r n+1) upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scattering resonances. This leads to an r n+1 lower bound on the counting function for scattering poles. |
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Keywords: | Asymptotically hyperbolic Poisson formula Resonances |
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