Inverse scattering results for manifolds hyperbolic near infinity

David Borthwick; Peter A. Perry

doi:10.1007/s12220-010-9149-9

Inverse scattering results for manifolds hyperbolic near infinity

David Borthwick, Peter A. Perry

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	305-333
Number of pages	29
Journal	Journal of Geometric Analysis
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s12220-010-9149-9
State	Published - Apr 2011

Bibliographical note

Funding Information:
D. Borthwick supported in part by NSF grant DMS-0901937. P.A. Perry supported in part by NSF grant DMS-0710477.

Funding

D. Borthwick supported in part by NSF grant DMS-0901937. P.A. Perry supported in part by NSF grant DMS-0710477.

Funders	Funder number
National Science Foundation (NSF)	DMS-0710477, DMS-0901937
Directorate for Mathematical and Physical Sciences	0710477, 0901937

Keywords

Hyperbolic
Inverse scattering
Resonance

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-010-9149-9

Cite this

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title = "Inverse scattering results for manifolds hyperbolic near infinity",

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.",

keywords = "Hyperbolic, Inverse scattering, Resonance",

author = "David Borthwick and Perry, {Peter A.}",

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AU - Perry, Peter A.

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N2 - 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.

AB - 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.

KW - Hyperbolic

KW - Inverse scattering

KW - Resonance

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Inverse scattering results for manifolds hyperbolic near infinity

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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