Title：Conical Kähler-Ricci flow

Speaker：刘佳伟  （马格德堡大学）

Abstract：Conical Kähler-Ricci flow was introduced to attack the existence problem of conical Kähler-Einstein metric which played an important role in the proof of Yau-Tian-Donaldson's conjecture. I will first talk about the  existence, uniqueness, regularity and convergence of conical Kähler-Ricci flow with weak initial data which admits L^p-density for some p> 1 on Kähler manifold. Furthermore, I will talk about the cusp Kähler-Ricci flow which is the limit flow of conical Kähler-Ricci flows when the cone angles tend to zero. Our motivation for considering these limit flows is to study the existence of Kähler-Einstein metrics when the cone angles tend to 0. At last, I will talk about the application of conical parabolic complex Monge-Amp/`ere equations. These lectures are joint works with X. Zhang and C. Zhang.