报告人：胥世成讲师

        首都师范大学

报告题目：Almost maximal volume entropy and local maximal volume on the universal cover

报告时间：2016年03月10日下午16:00

报告地点：海韵实验楼105

学院联系人:

报告摘要：Let $M$ be a closed Riemannian manifold. The volume entropy $h(M)$ of $M$ is defined to be the asymptotic exponential growth rate of the volume of balls centered at a fixed point $\tilde p$ in the universal cover $\tilde M$ as the radius goes to infinity. If the Ricci curvature of $M$ $\ge -(n-1)$, then $h(M)\le (n-1)$. It is proved by Ledrappier-Wang that volume entropy achieves maximum if and only if $M$ is isometric to a hyperbolic manifold. We prove that if $h(M)\ge (n-1-\epsilon)$, where $\epslion$ depends only on the diameter and dimension, then $M$ is Gromov-Hausdorff close and diffeomorphic to a hyperbolic manifold. In particular, $M$ won't collapse. We also prove that almost maximal volume entropy is equivalent to local maximal volume on the universal cover. Similar diffeo/isom rigidity holds for positive/nonnegative lower Ricci curvature bound. It is a joint work with Lina Chen and Xiaochun Rong.

报告人简介： 胥世成博士，现首都师范大学讲师，毕业于首都师范大学，于2010-2011及2012-2013年在南京大学做博士后，于2011-2012年在美国Iowa大学做访问助理教授。研究方向为微分几何与几何分析。

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