Time：14:00, Wednesday, October 11, 2022
Venue：E4-233
Host：Dr. Xin Fu, ITS
Speaker：Dr. Shengxuan Zhou, Peking Univerity
Title: The topological stability and unstability of tori with lower Ricci bound
Abstract：
In this talk, I will introduce a topological stability result given by Bruè-Naber-Semola [BNS23]. They proved that the Gromov-Hausdorff limit of a sequence of Riemannian metrics on torus with bounded diameter and sectional curvature lower bound is a topological torus. Then they pose a question: can we replace the sectional curvature lower bound by Ricci curvature lower bound? In the 3-dimension case, they give an affirmative answer. Then I will describe why the answer of this question should be negative in higher dimension case.
Reference: [BNS23] E. Bruè, A. Naber, D. Semola: Stability of Tori under Lower Sectional Curvature, preprint. https://arxiv.org/abs/2307.03824.
[Z23] S. Zhou: On the Gromov-Hausdorff limits of Tori with Ricci curvature lower bound, preprint. https://arxiv.org/abs/2309.10997.
