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

2024/06/04 by Ovidiu Munteanu, Jiaping Wang, Munteanu, Ovidiu +1 · 2 citations
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2406.02516

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.

Cited by

• Geometric Rigidity via Almost-Harmonic Twisted Spinors
• Level sets of harmonic functions on three-dimensional manifolds with nonnegative scalar curvature

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