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发表时间:2020-06-25 阅读次数:505次
报告题目: Recent progress on the Chern conjecture for isoparametric hypersurfaces in spheres
报 告 人:彦文娇
报告人所在单位:北京师范大学
报告日期:2020-06-25 星期四
报告时间:15:00-16:00
报告地点:腾讯会议ID: 446 317 564, 密码: 23456
  
报告摘要:

      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.

 

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本年度学院报告总序号:70

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