报告人：郝天泽(北京大学）

时间：2023年11月08日 10:00-

腾讯会议ID: 371 217 988

摘要：As a classic result about manifolds with positive lower bound of scalar curvature, Llarull theorem shows there is no greater metric than the standard metric on S^n with larger scalar curvature. In Gromov’s article about scalar curvature, he 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 our paper, without assumption that manifolds being spin, we prove that if a compact orientable Riemannian manifold (Mn, g) with scalar curvature Rg ≥ 6 admits an non-zero degree and 1-Lipschitz map to S^3 × T^{n-3}  (4≤n≤7), then (Mn, g) is locally isometric to the standard product metric on S^3 × T^{n-3}. Similar results are established for noncompact cases as S^3 × R^{n-3} being model spaces. We observe that the results are quite different when n = 4 and n ≥ 5. We also give a counterexample to ×Rm-Stabilized Mapping Theorem in Gromov’s article. These results reflect the phenomenon that one cannot increase the scalar curvature and meanwhile enlarge the manifold in all directions in some natural condition. The talk is based on the joint work with Prof. Yuguang Shi and postdoc Yukai Sun.

简介：郝天泽，现于北京大学数学科学学院就读博士学位，导师为史宇光教授，研究方向为数量曲率相关的微分几何问题。2013、2014年获CMO金牌。2019届北京大学优秀本科毕业生。曾获第五届阿里巴巴数学竞赛金奖.

邀请人：周恒宇

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