Sharp bottom spectrum and scalar curvature rigidity
Differential Geometry
2025-09-01 v3 Operator Algebras
Abstract
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.
Cite
@article{arxiv.2408.08245,
title = {Sharp bottom spectrum and scalar curvature rigidity},
author = {Jinmin Wang and Bo Zhu},
journal= {arXiv preprint arXiv:2408.08245},
year = {2025}
}
Comments
37 pages, minor changes