Bounds on the volume entropy and simplicial volume in Ricci curvature L^p bounded from below

2008/10/01 by Erwann Aubry, Aubry, E.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.0810.0149

openalex publication_date 2008/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a compact manifold with Ricci curvature almost bounded from below and π:M→ M be a normal, Riemannian cover. We show that, for any nonnegative function f on M, the means of føπ on the geodesic balls of M are comparable to the mean of f on M. Combined with logarithmic volume estimates, this implies bounds on several topological invariants (volume entropy, simplicial volume, first Betti number and presentations of the fundamental group) in Ricci curvature L^p-bounded from below.

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