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