几何和物理中的若干变分问题与发展问题

This project is focusing on studying some variational problems and evolution problems in geometry and physics. There are mainly two parts. The first part is studying the interior and boundary regularity theory and blow up analysis for certain critical elliptic systems with a structure that is more general than an anti-symmetric structure and applying it to harmonic maps from surfaces into general pseudo-Riemannian manifolds as well as some other harmonic map type systems. The second part is studying the geometric analysis aspects of Dirac-harmonic maps, super-Liouville equations and their generalizations.

本项目主要研究几何和物理中的一些变分问题与发展问题。主要分为两个部分。第一部分是研究具有比反对称更一般的结构的二阶椭圆系统临界情形的内部和边界正则性理论和 Blow up 分析理论并应用到从曲面到一般的伪黎曼流形的调和映照及其他一些调和映照类型的系统。第二部分研究 Dirac-调和映照，super-Liouville方程及其推广的几何分析性质。

本项目研究了几何和物理中的一些变分问题与热流问题。研究了一些调和映照类型椭圆系统的正则性和爆破分析，研究了Dirac-调和映照热流，super-Liouville方程及super-Toda系统的几何分析性质。相关成果一共发表18篇科研论文在JDG，JEMS，CMP等国际一流期刊。