Scattering on asymptotically hyperbolic manifolds
Abstract
In this thesis we use the method introduced by Vasy for analyzing the Laplacian on asymptotically hyperbolic spaces. This method in particular constructs the analytic continuation of the resolvent. I extend Vasy's method to the case of even metrics of order O(x2k+1 ), k ≥ 2 (in the sense of Guillarmou). Since the Laplacian is no longer smooth as in Vasy's analysis, I have to work with the calculus of non-smooth pseudodifferential operators. I proved high energy resolvent estimates in strips on asymptotically hyperbolic spaces when the metric is not necessarily even (in the sense of Guillarmou).
Degree
Ph.D.
Advisors
Sa Barreto, Purdue University.
Subject Area
Mathematics
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