The topological stability and unstability of tori with lower Ricci bound

2023-10-10 08:51:04

时间:2023年10月11日(星期三)14:00

地点:E4-233


主持人:西湖大学理论科学研究院 傅鑫

主讲人:北京大学 周胜铉

报告主题:The topological stability and unstability of tori with lower Ricci bound

报告摘要:

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.