On scalar curvature lower bounds and scalar curvature measure

2021/10/14 by John Lott, Lott, John · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2110.07551

openalex publication_date 2021/10/14 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.

Cited by

• Ricci-DeTurck flow of almost continuous L²-metrics, and metrics with distributional scalar curvature bounded from below
• Scalar curvature and Dirac operator for some singular spaces

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• A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature
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• Scalar curvature lower bounds on asymptotically flat manifolds