Lecturer：Li Yuxiang

Abstract:

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 $R\in L^2$.

Introduction to the Lecturer:

Li Yuxiang, Professor of Mathematicsand doctoral supervisor ofTsinghua University，in the research on：geometry analysis.

Invitee:

Li Gang Professor from School of Mathematics

Time:

8:30-9:30,Sep 06(Monday)

Venue:

Tencent Meeting, Meeting ID:935 988 457

Hosted by the School of Mathematics, Shandong University