题目：Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound

报告人: 胥世成(首都师范大学)

报告时间：2023年4月14日16：00-17：30

报告地点：五教5405

报告摘要：

The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian n-manifold with a negative lower Ricci curvature bound and a upper diameter bound, it was known that it admits an almost maximal volume entropy if and only if it is diffeomorphic and Gromov-Hausdorff close to a hyperbolic space form. We prove the quantitative rigidity of almost maximal volume entropy for RCD-spaces with a negative lower Ricci curvature bound and Riemannian manifolds with a negative Lp-integral Ricci curvature lower bound.