Llarull type theorems on complete manifolds with positive scalar curvature

：郝天泽（北京国际数学研究中心）
：2025-09-22 14:30
：海韵园实验楼S106

报告人：郝天泽（北京国际数学研究中心）

时  间：2025年9月22日14:30

地  点：海韵园实验楼S106

内容摘要:

Llarull theorem shows there is no greater metric than the standard metric on S^n with larger scalar curvature. Gromov mentioned that if there are the similar results on the product space of manifolds with positive curvature and R^n or other space forms. In this talk, without assumption that manifolds being spin, we discuss about such results for S^3 × R^{n-3} and the phenomenon is quite different when n = 4 and n ≥ 5. Our results imply the epsilon-gap length extremality of the standard S^3 is stable under the Riemannian production with R^m (1 ≤ m ≤ 4). The talk is based on the joint work with Prof. Yuguang Shi and Yukai Sun.

个人简介：

郝天泽，北京国际数学研究中心博士后。2025年7月在北京大学获得博士学位，导师是史宇光教授。2023年曾获第五届阿里巴巴国际数学竞赛金奖。郝天泽的研究领域是几何分析，特别是与数量曲率相关的几何问题，相关带数量曲率下界的完备流形拓扑与几何限制问题与刚性的成果发表在Trans. AMS, Symmetry Integrability Geom. Methods Appl.等期刊。

 

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