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].

报告时间：2021年3月9日15:00-

地点:勤园21-304教室

报告人简介：

盛为民，浙江大学数学科学学院教授，博士生导师，副院长。主要研究方向为共形几何，几何曲率流及其应用。先后主持国家自然科学基金重点项目，面上项目等多个基金项目，在Duke，JEMS，JDG，Math Ann等国际著名杂志发表科研论文多篇。