For an asymptotically hyperbolic metric on the interior of a compact manifold
with boundary, we prove that the resolvent and scattering operators are
continuous functions of the metric in the appropriate topologies.Comment: 21 pages, AMS-LaTe

Borthwick, David

English

arXiv

. For an asymptotically hyperbolic metric on the interior of a compact manifold with boundary, we prove that the resolvent and scattering operators are continuous functions of the metric in the appropriate topologies. Contents  1. Introduction 1 2. The hyperbolic model 4 3. Stretched products and distributions 5 3.1. Stretched product 5 3.2. Distributions 7 3.3. Symbol map 10 3.4. Normal operator 11 4. Resolvent and scattering operator 12 5. Continuity 16 5.1. The half-plane Re i  n=2 16 5.2. Extension to the whole plane 20 References 21 1. Introduction  Let X be a compact manifold with boundary and g an asymptotically hyperbolic metric on the interior of X , in the sense that all sectional curvatures approach \Gamma1  at @X. We will assume that g is of the form  g = ae  \Gamma2  h;  where ae is a boundary defining function on X and h is a Riemannian metric on  X . Such a metric g is necessarily complete. The asymptotic curvature condition reduces to jdaej h = 1 on @X. Any compact mani..

David Borthwick

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Scattering Theory And Deformations Of Asymptotically Hyperbolic Metrics

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.7854

Scattering theory and deformations of asymptotically hyperbolic metrics

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