Total squared mean curvature of immersed submanifolds in a negatively curved space
- A+
：胥世成（首都师范大学）
：2022-03-30 14:00
：腾讯会议ID：6312466238（无密码）
报告人：胥世成（首都师范大学）
时 间：3月30日下午14:00
地 点：腾讯会议ID：6312466238（无密码）
内容摘要:
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.
个人简介：
胥世成博士，现首都师范大学副教授，毕业于首都师范大学，于2010-2011及2012-2013年在南京大学做博士后，于2011-2012年在美国Iowa大学做访问助理教授。研究方向为研究方向为黎曼几何。在Journal of Differential Geometry、Advances in Mathematics， Trans. Amer. Math. Soc.等期刊发表论文10余篇。
联系人：夏超
