Conservation law for harmonic mappings in higher dimensions

发布时间：2022-09-23 作者：浏览次数：

Speaker:	郭常予	DateTime:	2022年10月14日（周五）上午10:00-11:00
Brief Introduction to Speaker: 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，主持或参与多项国家、省部基金，在相关领域已发表学术论文30篇。		Place:	腾讯会议：384-495-761
Abstract: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.