报告人：Jürgen Jost教授

        Max-Planck-Institute for Mathematics in the Nature Sciences

报告题目：The Bernstein problem

报告时间：2016年04月04日上午10:00

报告地点：数理楼661

学院联系人:

报告摘要: The famous result of Bernstein says that an entire minimal graph over the Euclidean plane is affine linear. This is one of the most striking results in nonlinear partial differential equations. Many mathematicians, including Moser, De Giorgi, Almgren, Simons, Chern, Yau have worked on extending this result to higher dimensions and codimensions. The result holds for codimension 1 and dimension < 8, but otherwise there exist counterexamples by bombieri-de giorgi-giusti and lawson-osserman.

    In this talk, I shall link the Bernstein problem to other concepts and structures in geometry and geometric analysis. More precisely, I shall reduce it to a problem about  harmonic maps into spheres and Grassmann manifolds, and I shall show that the convex geometry of those spaces leads to new generalizations of the Bernstein theorem in any dimension and codimension.

    This talk is based on joint work with Xin Yuanlong and Yang Ling.

报告人简介：Jürgen Jost教授，德国自然科学院院士，德国马克斯-普朗克应用数学研究所现任所长。1986年国际数学家大会45分钟报告人。1993年获得德国科学基金会（DFG）的最高奖——莱布尼茨奖。1996年开始至今任德国马克斯-普朗克应用数学研究所所长。1998年被聘为莱比锡大学名誉教授。研究方向涵盖数学的众多方面以及交叉学科，包括几何分析，变分与偏微分方程，数学物理，复杂动力系统，神经网络，数学生物，数学哲学，经济与社会学等。发表专著十余本，论文200余篇，他引2000余次，其中包括Acta. Math., Invent. Math., Comm. Pure Anal. Math., J. Algebraic Geom., J. Differential Geom. 等国际超一流数学杂志论文若干篇。

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