复旦大学教授杨翎学术报告 6月3日上午

发布时间:2021-05-31浏览次数:10

报告题目:On Dirichlet problem for minimal graphs and Lawson-Osserman constructions

时间:2021-06-03 (星期四) 09:00 ~ 2021-06-03 (星期四) 10:00

地点:腾讯会议室 ID148 948 271

主讲:复旦大学教授杨翎

主办:数学与信息学院, 福建省分析数学及应用重点实验室, 数学研究中心

参加对象:相关专业师生

 

报告摘要:We develop the Lawson-Osserman's works on minimal graphs. Firstly, we construct a constellation of uncountably many Lawson-Osserman spheres,  which are minimal in Euclidean spheres and therefore generate Lawson-Osserman cones that correspond to Lipschitz but non-differentiable solutions to the minimal surface system.  Then, by the theory of autonomous systems in plane, we find for each Lawson-Osserman cone an entire minimal graph having it as tangent cone at infinity. Further, in addition to the truncated Lawson-Osserman cones, we discover infinitely many analytic solutions to the Dirichlet problem of minimal surfaces system for boundary data induced by certain Lawson-Osserman spheres. As a corollary, those Lawson-Osserman cones are non-minimizing. These behaviors are observed for the first time. This is the joint work with Prof. Xiaowei Xu and Yongsheng Zhang.

 

报告人简介:杨翎,复旦大学教授,主要研究领域为微分几何,已主持多项国家基金,包括国家优青及面上项目等;独立或与他人合作,在极小子流形研究方面取得一系列重要成果,如:极小图的高斯映射像问题;Area-minimizing Lawson-Osserman cones构造和刻画;self shrinkers的高斯映射刚性问题;调和映射的正则性问题与Bernstein问题;目前在J. Diff. Geom.,  Adv Math,  J. Math. Pures Appl., Trans. AMSCal. Var. PDE等国际权威数学期刊发表学术论文19篇。