Quantitative maximal local rewinding volume rigidity with Ricci curvature bound below
主 题: Quantitative maximal local rewinding volume rigidity with Ricci curvature bound below
报告人: Professor Xiaochun Rong (Rutgers University and Capital Normal University)
时 间: 2017-01-13 15:00 - 16:00
地 点: 理科一号楼 1114(数学所活动)
For a metric $r$-ball $B_r(x)$ in a Riemannian manifold, its local rewinding volume is the volume of $B_r(x^*)$, where $(U^*,x^*)\to B_r(x),x)$ is the Riemannian universal cover. A compact $n$-space form of constant curvature $H$ can be characterized as a compact $n$-manifold of Ricci curvature $\ge (n-1)H$ and every $\rho$-ball ($\rho$-fixed) achieves the maximal rewinding volume. We will report a recent work on manifolds of Ricci curvature $\ge (n-1)H$ and every $\rho$-ball almost achieves the maximal local rewinding volume. This is a join work with Lina Chen and Shicheng Xu of Capital Normal University.
