一、题目

Manifolds for which Huber's Theorem holds

二、主讲人

李宇翔

三、摘要

In this talk, we discuss the properties of conformal metrics with $\|R\|_{L^\frac{n}{2}}<+\infty$ on a punctured ball of a Riemannian manifold to find some geometric obstacles for Huber's theorem. We will show that when Huber's theorem holds, the volume density at each end is exact 1, which implies that Carron and Herzlich's Euclidean volume growth condition is also a necessary condition for Huber's Theorem. When the dimension is 4, we derive the $L^2$-integrability of Ricci curvature, which follows that the Pfaffian of the curvature is integrable and satisfies a Gauss-Bonnet-Chern formula. We also prove that the Gauss-Bonnet-Chern formula proved by Lu and Wang, under the assumption that the second fundamental form is in $L^4$, holds when $R\in L^2$.

四、主讲人简介

李宇翔，清华大学数学系教授，博士生导师，方向：几何分析。

五、邀请人

李刚 数学学院副教授

六、时间

9月6日（周一）8:30-9:30

七、地点

腾讯会议，会议ID：935 988 457

八、主办方

山东大学数学学院