Speaker: 周胜铉，北京大学

Inviter: 简旺键副研究员

Title: Gromov-Hausdorff limits of tori with Ricci conditions I

Language: Chinese

Time & Venue: 2024.08.25 09:30-10:30 腾讯会议：876-6294-1705

Abstract: Bruè-Naber-Semola proved that for a sequence of Riemannian manifolds with bounded diameter and sectional curvature lower bound, if they are all homeomorphic to a torus, then its Gromov-Hausdorff limit is a topological torus, which answers a question of Petrunin in the affirmative. They subsequently raise a question: can we replace the sectional curvature lower bound by Ricci curvature lower bound? In the three-dimensional case, they give an affirmative answer. In this talk, I will describe why the answer to this question should be negative in the higher dimensional case. In the case of four dimensions, if we assume that there is a uniform upper bound of Ricci curvature, we can also give an affirmative answer.