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 ID：148 948 271
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. AMS及Cal. Var. PDE等国际权威数学期刊发表学术论文19篇。