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 | |
| 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.
Funding
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.
| Funders | Funder number |
|---|---|
| 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 |
Keywords
- Geometric scattering
- isophasal manifold
ASJC Scopus subject areas
- Geometry and Topology