Conservation law for harmonic mappings in higher dimensions
数学专题报告
报告题目(Title)：Conservation law for harmonic mappings in higher dimensions
报告人(Speaker)：郭常予 教授 （山东大学数学与交叉科学研究中心教授）
地点(Place)：腾讯会议：466-467-680
时间(Time)：2022年5月19日上午10:00-11:00
邀请人(Inviter)：汪志威
报告摘要
It has been a longstanding open problem to find a direct conservation law for harmonic mappings into manifolds. In the late 1980s, Chen and Shatah independently found a conservation law for weakly harmonic maps into spheres, which can be interpreted by Noether's theorem. This leads to Helein's celebrated regularity theorem on weakly harmonic maps from surfaces. For general target manifolds, Riviere discovered a direct conservation law in two dimension in 2007, allowing him to solve two well known conjectures of Hildebrandt and Heinz. As observed by Riviere-Struwe in 2008, due to lack of Wente's lemma, Riviere's approach does not extend to higher dimensions. In a recent joint work with Chang-Lin Xiang, we successfully found a conservation law for a class of weakly harmonic maps into general closed manifolds in higher dimensions. As an application, we obtain bubbling analysis for this class of maps in higher dimensions.
主讲人简介
郭常予，山东大学数学与交叉科学研究中心教授，博士生导师。2009年6月本科毕业于北京师范大学，2013年12月博士毕业于芬兰于韦斯屈莱大学。主要从事复分析、几何分析与非光滑分析相关研究，主持多项国家基金，在相关方向已发表学术论文近30篇。
