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【校庆70周年系列讲座】韩 青:Solutions of the Minimal Surface Equation and of the Monge-Ampere Equation near Infinity

 

讲座编号:jz-yjsb-2020-y013

讲座题目:Solutions of the Minimal Surface Equation and of the Monge-Ampere Equation near Infinity

主 讲 人:    美国圣母大学

讲座时间:20200925日(星期五)上午09:30

讲座地点:线上平台:腾讯会议,会议ID: 707 245 660

参加对象:数学与统计学院全体师生

主办单位:研究生院

承办单位:数学与统计学院

主讲人简介:

韩青,美国圣母大学数学系教授。美国纽约大学库朗数学研究所博士,美国芝加哥大学博士后,曾在德国莱比锡马普所和美国纽约大学库朗数学研究所进行科研。获美国Sloan Research Fellowship. 韩青教授长期致力于非线性偏微分方程和几何分析的研究工作,在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程等方面做出了一系列原创性的重要研究成果。

主讲内容:

Classical results assert that, under appropriate assumptions, solutions near infinity are asymptotic to linear functions for the minimal surface equation and to quadratic polynomials for the Monge-Ampere equation for dimension n at least 3, with an extra logarithmic term for n=2. We characterize remainders in the asymptotic expansions the difference between solutions and linear functions and the difference between solutions and quadratic polynomials for the Monge-Ampere equation by a single function, which is given by a solution of some elliptic equation near the origin via the Kelvin transform. Such a function is smooth in the entire neighborhood of the origin for the minimal surface equation in every dimension and for the Monge-Ampere equation in even dimension, but only C^{n-1,/alpha} for the Monge-Ampere equation in odd dimension, for any /alpha in (0,1).