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

Author:

Tadashi Fujioka

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Metric Geometry (math.MG)

journal:

date:

2023-06-19 16:00:00

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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