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A lower bound for the curvature integral under an upper curvature bound (2306.11577v3)
Published 20 Jun 2023 in math.DG and math.MG
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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