Speaker: Shi Yuguang,Professor, School of Mathematical Sciences, Peking University

Date: Nov.17, 2021

Time: 8:30-9:30

Location: Tencent Meeting, ID:618 908 522

Sponsor: School of Mathematics, Shandong University

Abstract:

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 a deep relation with positive mass theorem, in this talk I will talk about some known results related to this topic. My talk is based on my joint works with Dr.Wang Wenlong, Dr.Wei Guodong，Dr.Zhu Jintian, Dr.Liu Peng.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/158387.htm