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Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound.
- Source :
-
Journal of Functional Analysis . Jul2024, Vol. 287 Issue 2, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CURVATURE
*HYPERBOLIC spaces
*GREEN'S functions
*GEOMETRIC rigidity
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 287
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 177063171
- Full Text :
- https://doi.org/10.1016/j.jfa.2024.110457