Improved relative volume comparison for integral Ricci curvature and applications to volume entropy
Differential Geometry
2021-12-20 v5
Abstract
We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in \cite{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 \cite{Au2} and give an application on the algebraic entropy of its fundamental group. We also extend the almost minimal volume rigidity of \cite{BBCG} to integral Ricci curvature.
Keywords
Cite
@article{arxiv.1810.05773,
title = {Improved relative volume comparison for integral Ricci curvature and applications to volume entropy},
author = {Lina Chen and Guofang Wei},
journal= {arXiv preprint arXiv:1810.05773},
year = {2021}
}
Comments
11pages