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

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.

arXiv commentadded Section 1.2, Example 3.5, Lemma 5.2, a simplified proof of Proposition 5.4, and many other details and explanations

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