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arXiv · 2306.11577

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

Tadashi Fujioka
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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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Tadashi Fujioka. 2023-06-20. A lower bound for the curvature integral under an upper curvature bound. https://doi.org/10.1090/spmj%2F1858

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