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.
|Number of pages||29|
|Journal||Journal of Geometric Analysis|
|State||Published - Apr 2011|
Bibliographical noteFunding Information:
D. Borthwick supported in part by NSF grant DMS-0901937. P.A. Perry supported in part by NSF grant DMS-0710477.
- Inverse scattering
ASJC Scopus subject areas
- Geometry and Topology