一、题目

Positive mass theorem and Gromov’s fill-ins problem

二、主讲人

史宇光

三、摘要

Let $(\Sigma,\gamma)$ be an (n-1)-dimensional orientable Riemannian manifold, $H$ be a positive function on $\Sigma$, Gromov’s fill-ins problem is to ask: under what conditions $\gamma$ is induced by a Riemannian metric $g$ with nonnegative scalar curvature, for example, defined on $\Omega$, and $H$ is the mean curvature of $\Sigma$ in $(\Omega,g)$ with respect to the outward unit normal vector? By the recent result due to P.Miao we know such a $H$ cannot be too large, so the next natural question is what is“optimal” $H$ so that such a fill-in for the triple $(\Sigma,\gamma, H)$ exits ? it turns out that the problem has deep relation with positive mass theorem, in this talk I will talk about some known results relate to this topic. My talk is based on my joint works with Dr.Wang Wenlong, Dr.Wei Guodong，Dr.Zhu Jintian, Dr.Liu Peng.

四、主讲人简介

史宇光，北京大学数学科学学院教授，研究方向是几何分析。史教授是调和映照、正质量定理、正数量曲率问题和等周问题等问题方面的专家。2007年获国家杰出青年基金项目资助；2010年获第十一届中国青年科技奖；2010年获Ramanujan奖；2010-2013年主持国家基金委重大项目；2016年享受政府特殊津贴。

五、邀请人

李刚 数学学院副教授

六、时间

11月17日（周三）8:30-9:30

七、地点

腾讯会议，会议ID：618 908 522

八、主办方

山东大学数学学院