学术科研-Geometry & Topology Seminar

Singular metric and scalar curvature

Abstract

A classical Theorem in conformal geometry states that on a closed manifold with non-positive Yamabe invariant, a smooth metric which attains the invariant must be Einstein. In this talk, we will discuss the extension to continuous metrics with high co-dimensions singularity. This resolves a conjecture of Schoen in the category of continuous metrics. This is a joint work with L.-F. Tam.

报告人简介：李文俊(Lee, Man-Chun)，香港中文大学助理教授。2018 年于香港中文大学取得博士学位，之后先后在 UBC、Northwestern、Warwick 从事博士后研究工作。研究方向为几何分析，特别是在复几何领域做出多项创新性工作。其工作发表在Geom. Topol.、J. Differential Geom.、Calc. Var. Partial Differential Equations、 J. Funct. Anal. 、Math. Ann.、Trans. Amer. Math. Soc.、IMRN 等国际知名期刊上。