A lower bound for the curvature integral under an upper curvature bound

2023/06/20 by Tadashi Fujioka, Fujioka, Tadashi
Mathematics · #53B21 #53C20 #53C21 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.11577

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the integral of scalar curvature over a Riemannian manifold is uniformly bounded below in terms of its dimension, upper bounds on sectional curvature and volume, and a lower bound on injectivity radius. This is an analogue of an earlier result of Petrunin for Riemannian manifolds with sectional curvature bounded below.

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