报告人简介：

沈伟明，研究方向偏微分方程与几何分析。2011年本科毕业于东华大学。2016年博士毕业于北京大学数学科学学院，导师韩青教授。之后在北京大学数学中心做金光博士后，合作导师田刚院士。2018年8月入职首都师范大学数学科学学院。

报告摘要：

In this talk, we study the properties of the first global termin the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying domain is a disc. More generally, we prove some gap theorems relating such a boundary integral to the number of components of the boundary. We also give some positive mass theorem type results through the integral of the global coefficient. I will also mention some progress on high dimension at the end of this talk.

报告主持：秦玉明