Inverse scattering results for manifolds hyperbolic near infinity
arXiv:0906.0542
Abstract
We study the inverse resonance problem for conformally compact manifolds which are hyperbolic outside a compact set. Our results include compactness of isoresonant metrics in dimension two and of isophasal negatively curved metrics in dimension three. In dimensions four or higher we prove topological finiteness theorems under the negative curvature assumption.
25 pages. v3: Minor corrections, references added