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.
会议网址：https://meeting.tencent.com/s/qGfQJBBUx2Dv
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彦文娇，北京师范大学数学科学学院教授，优秀青年基金获得者。2012年在北京师范大学获得理学博士学位，2014年至2016年获得日本学术振兴会资助访问日本东北大学从事博士后研究。主要研究方向为微分几何，特别是等参超曲面，等参函数及相关应用的研究。其研究成果发表在J. Diff. Geom. 、Advances in Math. 、J. Funct. Anal.、IMRN等著名国际学术期刊上。主持国家自然科学优秀青年基金等项目。
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