Total squared mean curvature of immersed submanifolds in a negatively curved space
数学专题报告
报告题目(Title)：Total squared mean curvature of immersed submanifolds in a negatively curved space
报告人(Speaker)：胥世成
地点(Place)：腾讯会议 ID：223-372-906
时间(Time)：2022 年 04 月 08 日（周五） 15:00--16:00
邀请人(Inviter)：苏效乐，王雨生
报告摘要
Let n≥2 and k≥1 be two integers. Let M be an isometrically immersed closed submanifold of dimension n and co-dimension k, which is homotopic to a point, in a complete manifold N, where the sectional curvature of N is no more than δ<0. We prove that the total squared mean curvature of M in N and the first non-zero eigenvalue λ_1(M) satisfies λ_1(M)≤ n(δ +Vol^(-1)(M)) ∫ |H|^2 dvol.
The equality implies that M is minimally immersed in a geodesic sphere after lifted to the universal cover of N. This completely settles an open problem raised by E. Heintze in 1988. This is a joint work with Yanyan Niu.
主讲人简介
胥世成，首都师范大学副教授，黎曼几何与度量几何专家，研究成果部分发表在 JDG 和 Adv. in Math. 上。
