Title：The Rigidity and Gap Theorem for Liouville's Equation

Speaker：Weiming Shen （Peking University）

Time：2018年4月27日（周五）    下午 16:00-17:30

Room：东区管理科研楼   数学科学学院1418室

Abstract：In this talk, I will talk about the properties of the first global term in 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. The conformal structure plays an essential role.