Almost maximal volume entropy rigidity for integral Ricci curvature in the non-collapsing case

2022/01/20 by Lina Chen, Chen, Lina
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.08134

openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we will show the almost maximal volume entropy rigidity for manifolds with lower integral Ricci curvature bound in the non-collapsing case: Given n, d, p>(n)/(2), there exist δ(n, d, p), ε(n, d, p)>0, such that for δ0, then M is diffeomorphic and Gromov-Hausdorff close to a hyperbolic manifold where δ, ε also depends on v.

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