题目: Splitting theorems under intermediate curvatures      

报告人：洪寒（北京交通大学）

报告时间：2026年6月4日16：00-17：00

报告地点：腾讯会议937 689 208

摘要: In this talk, we will show several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either$ 3≤n≤5, 1≤m≤n−1$, or $6≤n≤7, m\in{1,n−1,n−2}$, any manifold of the topological type $M^{n−m}×T^{m−1}×R$ with nonnegative m-intermediate curvature is isometrically covered by the canonical product $M×R^m$. We also construct smooth metrics on such manifolds with uniformly positive m-intermediate curvature for $6≤n≤7, 2≤m≤n−3$.  The proof is based on a new recursion theorem for spectral intermediate curvatures and cylindrical splitting theorems. In particular, when $m=n−1$, it provides a new proof of some results by Chodosh--Li  and Zhu. Moreover, the recursion theorem can be used to reprove a result of Brendle--Hirsch--Johne.

个人简介：洪寒，博士毕业于加拿大英属哥伦比亚大学。清华大学丘成桐数学科学中心博士后，现为北京交通大学副教授。主要研究方向为微分几何与几何分析，研究兴趣为极小曲面等相关问题。