Isoscattering deformations for complete manifolds of negative curvature

Peter Perry; Dorothee Schueth

doi:10.1007/BF02922135

Isoscattering deformations for complete manifolds of negative curvature

Peter Perry, Dorothee Schueth

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	661-677
Number of pages	17
Journal	Journal of Geometric Analysis
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/BF02922135
State	Published - 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

Access to Document

10.1007/BF02922135

Cite this

@article{27e24ae695e4466e916e89c626207a9c,

title = "Isoscattering deformations for complete manifolds of negative curvature",

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.",

keywords = "Geometric scattering, isophasal manifold",

author = "Peter Perry and Dorothee Schueth",

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.",

year = "2006",

doi = "10.1007/BF02922135",

language = "English",

volume = "16",

pages = "661--677",

number = "4",

}

TY - JOUR

T1 - Isoscattering deformations for complete manifolds of negative curvature

AU - Perry, Peter

AU - Schueth, Dorothee

N1 - 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.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Geometric scattering

KW - isophasal manifold

UR - http://www.scopus.com/inward/record.url?scp=84867982318&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867982318&partnerID=8YFLogxK

U2 - 10.1007/BF02922135

DO - 10.1007/BF02922135

M3 - Article

AN - SCOPUS:84867982318

VL - 16

SP - 661

EP - 677

IS - 4

ER -

Isoscattering deformations for complete manifolds of negative curvature

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this