Isoscattering deformations for complete manifolds of negative curvature

Peter Perry, Dorothee Schueth

Research output: Contribution to journalArticlepeer-review

Abstract

We construct continuous families of nonisometric metrics on simply connected manifolds of dimension n ≥ 9which have the same scattering phase, the same resolvent resonances, and strictly negative sectional curvatures. This situation contrasts sharply with the case of compact manifolds of negative curvature, where Guillemin/Kazhdan, Min-Oo, and Croke/Sharafutdinov showed that there are no nontrivial isospectral deformations of such metrics.

Original languageEnglish
Pages (from-to)661-677
Number of pages17
JournalJournal of Geometric Analysis
Volume16
Issue number4
DOIs
StatePublished - 2006

Bibliographical note

Funding Information:
Math SubjecCt lassifications5.8 J53, 58J50. Key Wordsa ndP hrases.G eometric scattering, isophasal manifold. Acknowledgemeanntsd Notes. The first author was supported in part by NSF grant DMS-0100829 and DMS-0408419; second author was supported in part by the DFG Priority Programme 1154.

Keywords

  • Geometric scattering
  • isophasal manifold

ASJC Scopus subject areas

  • Geometry and Topology

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