The wave equation on asymptotically de Sitter-like spaces |
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Authors: | Andrá s Vasy |
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Affiliation: | Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, CA 94305-2125, USA |
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Abstract: | In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X○,g) which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y±, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to +∞, and to the other manifold as the parameter goes to −∞, we also define the scattering operator, and show that it is a Fourier integral operator associated to the bicharacteristic flow from Y+ to Y−. |
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Keywords: | 35L05 58J45 |
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