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arXiv · 2408.08245

Sharp bottom spectrum and scalar curvature rigidity

Jinmin Wang·Bo Zhu
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Abstract

We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with a 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.

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Jinmin Wang, Bo Zhu. 2024-08-15. Sharp bottom spectrum and scalar curvature rigidity. https://arxiv.org/abs/2408.08245

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