题目：Recent Progress on the Chern Conjecture for Isoparametric Hypersurfaces in Spheres

报告人：彦文娇 教授（北京师范大学）

地址：腾讯会议室（详见网页）

时间：2020年7月3日 14:00-15:00

地点：https://meeting.tencent.com/s/ksamPH75UuJ3

会议 ID：943 722 042

摘要：In this talk, we will first recall some background and research history of Chern's conjecture,

which asserts that a closed, minimally immersed hypersurface of the unit sphere Sn+1(1) with constant scalar

curvature is isoparametric. Next, we introduce our progress in this conjecture. We proved that for a closed hypersurface Mn ⊂ Sn+1(1) with constant mean curvature and constant non-negative scalar curvature, if tr(Ak) are constants (k = 3,...,n−1) for shape operator A, then M is isoparametric, which generalizes the theorem of de Almeida and Brito in their 1990's paper in 《Duke Math. J. 》 for n = 3 to any dimension n, strongly supporting Chern’s conjecture. This talk is based on two joint papers with Professor Dongyi Wei and Professor Zizhou Tang.

欢迎各位参加！