Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929373627547648 |
|---|---|
| author | Munteanu, Ovidiu Wang, Jiaping |
| author_facet | Munteanu, Ovidiu Wang, Jiaping |
| contents | A classical result of Cheng states that the bottom spectrum of complete manifolds of fixed dimension and Ricci curvature lower bound achieves its maximal value on the corresponding hyperbolic space. The paper establishes an analogous result for three-dimensional complete manifolds with scalar curvature lower bound subject to some necessary topological assumptions. The rigidity issue is also addressed and a splitting theorem is obtained for such manifolds with the maximal bottom spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound Munteanu, Ovidiu Wang, Jiaping Differential Geometry Analysis of PDEs A classical result of Cheng states that the bottom spectrum of complete manifolds of fixed dimension and Ricci curvature lower bound achieves its maximal value on the corresponding hyperbolic space. The paper establishes an analogous result for three-dimensional complete manifolds with scalar curvature lower bound subject to some necessary topological assumptions. The rigidity issue is also addressed and a splitting theorem is obtained for such manifolds with the maximal bottom spectrum. |
| title | Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2406.02516 |