Isoscattering Schottky manifolds

Robert Brooks, Ruth Gornet, Peter Perry

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We exhibit pairs of infinite-volume, hyperbolic three-manifolds that have the same scattering poles and conformally equivalent boundaries, but which are not isometric. The examples are constructed using Schottky groups and the Sunada construction.

Original languageEnglish
Pages (from-to)307-326
Number of pages20
JournalGeometric and Functional Analysis
Volume10
Issue number2
DOIs
StatePublished - 2000

Bibliographical note

Funding Information:
Acknowledgements. Robert Brooks gratefully acknowledges the hospitality of the University of Kentucky. Ruth Gornet acknowledges the hospitality of the University of Kentucky where her work was supported by Texas Tech University and the National Science Foundation through a POWRE Fellowship. Peter Perry gratefully acknowledges the hospitality of the Department of Mathematics, Technion{Israel Institute of Technology, where part of this work was carried out.

Funding Information:
R.B. supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, the Fund for the Promotion of Research at the Technion, the New York Metropolitan Fund, and the NSF-CNRS program in \Inverse Spectral Geometry". R.G. supported in part by NSF Grant DMS 97-53220 and the NSF-CNRS program in \Inverse Spectral Geometry". P.P. supported in part by NSF Grant DMS 97-07051.

Funding

Acknowledgements. Robert Brooks gratefully acknowledges the hospitality of the University of Kentucky. Ruth Gornet acknowledges the hospitality of the University of Kentucky where her work was supported by Texas Tech University and the National Science Foundation through a POWRE Fellowship. Peter Perry gratefully acknowledges the hospitality of the Department of Mathematics, Technion{Israel Institute of Technology, where part of this work was carried out. R.B. supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, the Fund for the Promotion of Research at the Technion, the New York Metropolitan Fund, and the NSF-CNRS program in \Inverse Spectral Geometry". R.G. supported in part by NSF Grant DMS 97-53220 and the NSF-CNRS program in \Inverse Spectral Geometry". P.P. supported in part by NSF Grant DMS 97-07051.

FundersFunder number
Japan Society for the Promotion of Science Fund for the Promotion of Joint International Research
NSF-CNRS
New York Metropolitan Fund
National Science Foundation Arctic Social Science ProgramDMS 97-53220, DMS 97-07051
Texas Tech University Health Sciences Center at Dallas
Israel Academy of Sciences and Humanities
US-Israel Binational Science Foundation
Technion - Israel Institute of Technology

    ASJC Scopus subject areas

    • Analysis
    • Geometry and Topology

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