题 目: Properness of energy functions on polarized compactifications of reductive Lie groups
摘 要: In this talk, I will first give an introduction on Tian's properness conjecture concerning on an analytic characterization of the existence of canonical metrics in Kahler geometry. Then I will focus on compactifications of reductive Lie groups. The main results are criterion theorems of the properness of two important functionals——Ding functional and Mabuchi's K-energy on these manifolds. In particular, the existence of Kahler-Einstein metrics, Kahler-Ricci solitons and Mabuchi's generalized Kahler-Einstein metrics on Fano compactifications of reductive Lie groups can be established. More generally, for constant scalar curvature metrics case, we will obtain the existence of weak minimizers in the sense of convex potentials.
邀请人 ： 许奕彦 老师