Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound
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.
Cite
@article{arxiv.2406.02516,
title = {Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound},
author = {Ovidiu Munteanu and Jiaping Wang},
journal= {arXiv preprint arXiv:2406.02516},
year = {2024}
}
Comments
The sharp spectral bound was initially included in arXiv:2201.05595 by the same authors; now it is part of this separate submission, which also covers rigidity results. Final version, to appear in Journal of Functional Analysis. 30 pages. arXiv:2201.05595 has been updated to reflect its new content