Improved relative volume comparison for integral Ricci curvature and applications to volume entropy

2018/10/13 by Lina Chen, Chen, Lina, Guofang Wei +1 · 1 citation
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 · pdf · doi:10.48550/arxiv.1810.05773

openalex publication_date 2018/10/13 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28

Abstract

We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in \citePW1. Using one of these volume comparisons, we derive an estimate for the volume entropy in terms of integral Ricci curvature which substantially improves an earlier estimate in \citeAu2 and give an application on the algebraic entropy of its fundamental group. We also extend the almost minimal volume rigidity of \citeBBCG to integral Ricci curvature.

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