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数智学术论坛: 彦文娇教授

baogaotimu:recent progress on the chern conjecture for isoparametric hypersurfaces in spheres

bao gao ren:yanwenjiao

baogaoshijian: 2021nian11yue23ri(zhouer)14:00-15:00

baogaodidian:tengxunhuiyi(huiyihao:481 410 211)

【报告人简介】

彦文娇,北京师范大学数学学院教授,博士生导师,国家优秀青年基金获得者。主要研究领域为微分几何,特别是等参超曲面、等参函数及其相关应用。代表性成果包括完全解决了等参情形的丘成桐第一特征值猜想,给出陈省身猜想在任意维数的部分进展等。主要研究成果均发表在J. Diff. Geom.,Advances in Math.,J. Funct. Anal.,IMRN,Comm. Anal. Geom.,Sci. China Math.,Math. Z.等国际著名数学期刊上。曾4次在中日几何会议(第8、9、11、14届)、日本数学会年会、韩国 NIMS 会议等国际学术会议上多次作学术报告。

【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.












撰稿:魏斯宁 审核:富宇 单位:数据科学与人工智能学院