The existence of weighted cscK metrics and G-coercivity of weighted Mabuchi functional
数学专题报告
报告题目(Title)：The existence of weighted cscK metrics and G-coercivity of weighted Mabuchi functional
报告人(Speaker)：刘亚雄（马里兰大学）
地点(Place)：腾讯会议：588-364-804
时间(Time)：2024年6月27日（周四）上午9:00-10:00
邀请人(Inviter)：张科伟
报告摘要
In this talk, we study weighted cscK in the sense of Lahdili, by variational approach and continuity method. We prove that on a smooth Kahler manifold, the G-coercivity of the weighted Mabuchi functional implies the existence of weighted-cscK (extremal) metric. Our key points are uniform C^0 estimate (following Guo-Phong’s argument), uniformly W^2,p-estimate (following Chen-Cheng), which enable us to generalize this result to the case of G-equivariant Q-Gorenstein smoothable projective klt varieties, and C^2-estimate (following Chen-Cheng). This is a joint work with Jiyuan Han.
