半空间上仿射极大方程的Liouville定理

2024.01.17

投稿:龚惠英部门:理学院浏览次数:

活动信息

报告题目 (Title): A Liouville theorem for the affine maximal equation on half-space

中文标题:半空间上仿射极大方程的Liouville定理

报告人 (Speaker):周斌(北京大学)

报告时间 (Time):2024年1月17日(周三) 17:00-18:00

报告地点 (Place):校本部GJ303

邀请人(Inviter):席东盟、李晋、张德凯,吴加勇

主办部门:理学院数学系

报告摘要:The famous affine Bernstein theorem, also called Chern’s conjecture, asserts that an affine maximal graph of a smooth, locally uniformly convex function on Euclidean space is a paraboloid. This conjecture was first proved by Trudinger-Wang in dimension two in 2000. One can easily find affine maximal graphs which are not paraboloid on half spaces. In this talk, we show a Liouville theorem for the affine maximal equation on half-spaces with certain assumptions. The proof is based on the study on the related linearized Monge-Amp\`ere equation and the Monge-Amp\`ere equation

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