报告人：艾万君 （西南大学）

时间：2022年06月03日10:30开始

腾讯会议ID：123 055 792

摘要：Harmonic maps are one of the most classical objects studied in geometry analysis. The existence, regularity and compactness (blow-up) of harmonic maps related variational problems are closely related and most concerned. The classical regularity theory of weakly harmonic maps was solved by Hélein, and further developed by Rivière and Struwe et al. In this talk, we will start from classical regularity results of spherical harmonic maps and Lorentz spherical harmonic maps, and then show some generalizations of these results for general target manifolds, both in Riemannian and Lorentzian cases. Finally, we present a new result about the regularity of Dirac-harmonic maps from Riemann surfaces into stationary Lorentzian manifolds. It turns out the regularity of weakly Dirac- harmonic maps depends on a general regularity theorem of critical elliptic systems without an L2-antisymmetric structure. Our results generalize the corresponding regularity results of Hélein, Rivière and Rivière-Struwe for harmonic maps. This is joint work with Zhu, Miaomiao.

简介：艾万君，2017 年毕业于中国科学技术大学。随后，在上海交通大学从事博士后研究工作。现任职于西南大学太阳成集团tyc539。承担重庆市面上项目、中央高校基本科研业务费项目各一项。参与国家自然科学基金面上项目两项、国家自然科学基金数学天元基金项目一项。主要研究领域为调和映射及其相关领域。相关研究结果发表在 J. Func. Anal.、Calc. Var. PDE.、Sci. China Math.、Ann. Global Anal. Geom. 等杂志上。

邀请人：林德燮 周恒宇

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