题目: A note about quantitative maximal volume entropy rigidity

报告人：陈丽娜（南京大学）

报告时间：2022/10/17（周一） 16:00-17:30 (GMT+08:00) 中国标准时间 - 北京

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#腾讯会议：962-748-616

摘要: With Xiaochun Rong and Shicheng Xu, we proved the quantitative maximal volume entropy rigidity which says that there is $\epsilon(n, D)>0$ such that for a compact $n$-manifold $M$ with diameter $\op{diam}(M)\leq D$, Ricci curvature $\op{Ric}_M\geq -(n-1)$, if the volume entropy $h(M)\geq n-1-\epsilon(n, D)$, then $M$ is diffeomorphic and Gromove-Hausdorff close to a hyperbolic manifold. In the proof there, to take care of the collapsing case, one need a property  that if the equivariant Gromov-Hausdorff limit space is a hyperbolic manifold and the cocompact limit isometry subgroup's identity component is nilpotent, then the identity component must be trivial (\cite[Theorem 2.5]{CRX}).  In this paper,  we will give a more general property about cocompact limit isometry subgroups in hyperbolic space form.  As an application of this property,  we obtain the quantitative maximal volume entropy rigidity for manifolds with integral Ricci curvature lower bound and $\RCD(-(n-1), n)$-spaces. This is a joint work with Shicheng Xu.