学术报告：2018年10月26日13：30-14：30，陈丽娜，华东师范大学几何中心

报告人

陈丽娜

单位

华东师范大学几何中心

报告题目

Quantitative Maximal Rigidity and Minimal Phenomenon of   Volume Entropy with Ricci Curvature Lower Bound

报告时间

10月26日

13：30-14：30

地点

第一报告厅

邀请人

王小六

报告摘要

Abstract:   For a compact manifold, the volume entropy always exists. And by Bishop   volume comparison, with Ricci curvature bounded below by –(n-1), the volume entropy   is not bigger than n-1. Ledrappier-Wang in 2011 showed that if a manifold   achieves the maximal volume entropy n-1, then it is isometric to a hyperbolic   manifold. In this talk, I will first report a work where we showed that if   the volume entropy is almost maximal, then the manifold is diffeomorphic and   Gromov-Hausdorff close to a hyperbolic manifold.

For a   compact manifold with small volume entropy, i.e., closed to 0, the Nilpotency   conjecture says that the fundamental group of the manifold contains a finite   index nilpotent subgroup. And in group growth theory, the modified Milnor's   problem asks that whether any finitely presented group of vanishing algebraic   entropy has at most polynomial growth. In this talk, we will show that a   positive answer to the modified Milnor's problem is equivalent to the   Nilpotency conjecture.

This talk   is based on the joint works with Professor Xiaochun Rong and Shicheng Xu.

报告人简介

陈丽娜，华东师范大学几何中心博士后，目前主要研究 Ricci 曲率有下界的黎曼流形上的几何拓扑性质，研究成果深刻，发表在J.   Diff. Geom.和Trans.   Amer. Math. Soc.等杂志上。