【偏微分方程系列报告】
报告题目：Removable singularity of positive mass theorem with continuous metrics
报告人：盛为民（教授），浙江大学
会议时间：2021/03/12 15:00-16:00
腾讯会议ID: 134 758 611
报告摘要：In this talk, I consider asymptotically flat Riemannnian manifolds $(M^n, g)$ with $C^0$ metric $g$ and $g$ is smooth away from a closed bounded subset $\Sigma$ and the scalar curvature $R_g\ge 0$ on $M\setminus \Sigma$. For given $n\le p\le \infty$, if $g\in C^0\cap W^{1,p}$ and the Hausdorff measure $\mathcal{H}^{n-\frac{p}{p-1}}(\Sigma)<\infty$ when $n\le p<\infty$ or $\mathcal{H}^{n-1}(\Sigma)=0$ when $p=\infty$, then I will show that the ADM mass of each end is nonnegative. Furthermore, if the ADM mass of some end is zero, then I'll show that $(M^n, g)$ is isometric to the Euclidean space by showing the manifold has nonnegative Ricci curvature in RCD sense. This result extends the result of Dan Lee and P. Lefloch (2015 CMP) from spin to non-spin, also improves the result of Shi-Tam [JDG 2002] and Lee [PAMS 2013]. Moreover, for $p=\infty$, this confirms a conjecture of Lee [PAMS 2013].
报告人简介：盛为民，浙江大学教授，博士生导师，数学科学学院副院长。研究兴趣是具有一定几何或物理背景的微分几何和偏微分方程，包括预定曲率问题，高阶Yamabe问题，以及曲率流问题。盛教授在Duke Math. J.、CVPDE、Math. Z.、CAG、JDG、JEMS、Math. Ann.、JGA等国际高水平刊物上已发表学术论文40余篇，主持国家自然科学基金面上项目4项，参与国家自然科学基金重点项目2项。
