Improved relative volume comparison for integral Ricci curvature and applications to volume entropy
Abstract
We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in PW1. 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 Au2 and give an application on the algebraic entropy of its fundamental group. We also extend the almost minimal volume rigidity of BBCG to integral Ricci curvature.
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