锐底谱和标量曲率刚度

arXiv - MATH - Operator Algebras Pub Date : 2024-08-15 DOI:arxiv-2408.08245

Jinmin Wang, Bo Zhu

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引用次数: 0

摘要

我们证明了具有标量曲率下限的几何可收缩流形上的拉普拉斯底谱的尖锐上界，并描述了相等时标量曲率的分布特征。此外，如果流形是封闭双曲流形的普遍盖，我们还证明了标量曲率刚性定理。

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Sharp bottom spectrum and scalar curvature rigidity

We prove a sharp upper bound for the bottom spectrum of Laplacian on geometrically contractible manifolds with scalar curvature lower bound, and characterize the distribution of scalar curvature when equality holds. Moreover, we prove a scalar curvature rigidity theorem if the manifold is the universal cover of a closed hyperbolic manifold.

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arXiv - MATH - Operator Algebras

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