非线性偏微分方程系列报告
报告1：
报告题目：Partial regularity theory for a fourth order elliptic system
报告人：向长林研究员（三峡大学、博士）
时间：2021.9.14（周二），14：30-16：30
地点：腾讯会议（ID：967408139）
摘要：I will discuss a partial regularity theory in dimension n≥5 for a fourth order elliptic system with critical nonlinearity which includes the equation of biharmonic mappings from Euclidean space into closed Riemannian manifolds. This problem is mainly motivated by the bubbling analysis of stationary harmonic mappings by F.-H. Lin and T. Riviere (Duke, 2002), and also by the Lp theory of R. Moser (TAMS, 2015) on stationary harmonic mappings and an expectation made by B. Sharp (MAA, 2014) on conformally invariant elliptic problems. It is a joint work with C.-Y. Guo and C. Wang.
个人简介：向长林，三峡大学数学研究中心研究员，2015年博士毕业于芬兰于韦斯屈莱大学（University of Jyvӓskylӓ）数学系。研究兴趣为椭圆型偏微分方程(组)正则性理论及其在几何中的应用，发表过多篇论文。
报告2：
报告题目：Compactness of harmonic maps between metric spaces and applications
报告人：郭常予教授（山东大学、博士生导师）
时间：2021.9.15（周三），9：00-11：00
腾讯会议：513 799 136
摘要：The well-known Schoen-Li-Wang conjecture states each quasiconformal self-homeomorphism of the boundary at infinity of a rank one symmetric space M extends to a unique harmonic map from M to itself. This conjecture has been solved recently in a series of breakthrough works. Benois-Hulin (Ann. Math. 2017) gave a proof independent of the theory of quasiconformal maps. Recently, Sidler-Wenger (J. Diff. Geom. 2021) further extended the Benois-Hulin’s theorem.
In this talk, we shall discuss the compactness property of energy minimizing harmonic maps and as an application, we remove the finite dimensional assumption in the main result of Sidler-Wenger. The talk is based on a joint work with Hui-Chun Zhang.
个人简介：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。主要研究方向为单复变-几何函数论、几何偏微分方程和奇异度量测度空间上的分析与几何。在相关领域已发表论文20余篇。
