Sharp bottom spectrum and scalar curvature rigidity

2024/08/15 by Wang, Jinmin, Zhu, Bo · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2408.08245

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.

Cited by

• Non-negative scalar curvature on spin surgeries and Novikov conjecture
• Geometric Rigidity via Almost-Harmonic Twisted Spinors

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