A lower bound for the curvature integral under an upper curvature bound
Differential Geometry
2025-07-17 v3 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2306.11577,
title = {A lower bound for the curvature integral under an upper curvature bound},
author = {Tadashi Fujioka},
journal= {arXiv preprint arXiv:2306.11577},
year = {2025}
}
Comments
added Section 1.2, Example 3.5, Lemma 5.2, a simplified proof of Proposition 5.4, and many other details and explanations