*主持人：叶东 教授
*时间：2020年10月30日13:00-14:00
*地点：腾讯会议 ID：331 930 398
*讲座内容简介：
In this talk, I will prove that if $u$ is a solution to the Liouville equation $$\Delta u+e^{2u} =0 \quad \mbox{in $\mathbb{R}^2$,}$$then the diameter of $\mathbb{R}^2$ under the conformal metric $g=e^{2u}\delta$ is bounded below by $\pi$. Here $\delta$ is the Euclidean metric in $\mathbb{R}^2$. Moreover, I will present a family of entire solutions to the Liouville equation such that the corresponding diameters of $\mathbb{R}^2$ range over $[\pi,2\pi]$. Then I will discuss the completion of $\mathbb{R}^$ with a conformal metric and show some geometric inequalities related to radial super solutions to the Liouville equation. I will also discuss some unsolved questions related to these results. This is a joint work with Professor Changfeng Gui.
*主讲人简介：
李沁峰，湖南大学副教授，2018年博士毕业于普渡大学，导师Monica Torres 和 Changyou Wang教授。2018年9月-2020年5月在美国UTSA从事博士后工作，导师桂长峰教授。在几何测度论、形状优化、Liouville 型方程等问题上取得了一些有意义的工作，成果发表在 CVPDE, Indiana Univ. Math. J, IMRN等知名期刊。
