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Relative volume comparison for integral Ricci curvature and some applications

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 نشر من قبل Lina Chen
 تاريخ النشر 2018
  مجال البحث
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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.



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