Sharp bottom spectrum and scalar curvature rigidity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909758695407616 |
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| author | Wang, Jinmin Zhu, Bo |
| author_facet | Wang, Jinmin Zhu, Bo |
| contents | We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound is achieved. Additionally, we prove a net characterization of scalar curvature for general complete noncompact Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp bottom spectrum and scalar curvature rigidity Wang, Jinmin Zhu, Bo Differential Geometry Operator Algebras We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound is achieved. Additionally, we prove a net characterization of scalar curvature for general complete noncompact Riemannian manifolds. |
| title | Sharp bottom spectrum and scalar curvature rigidity |
| topic | Differential Geometry Operator Algebras |
| url | https://arxiv.org/abs/2408.08245 |