Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound

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 curvat...

Full description

Saved in:
Bibliographic Details
Published inJournal of functional analysis Vol. 287; no. 2; p. 110457
Main Authors Munteanu, Ovidiu, Wang, Jiaping
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.07.2024
Subjects
Green's function
Scalar curvature
Spectrum
Scalar curvature
Green's function
Spectrum
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2024.110457