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

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	661-677
Número de páginas	17
Publicación	Journal of Geometric Analysis
Volumen	16
N.º	4
DOI	https://doi.org/10.1007/BF02922135
Estado	Published - 2006

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
Deutsche Forschungsgemeinschaft
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-0100829, DMS-0408419

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF02922135

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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.",

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AU - Schueth, Dorothee

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PY - 2006

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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

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -

Isoscattering deformations for complete manifolds of negative curvature

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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