2014/12/04 by Jin, Xishen, Liu, Jiawei, Zhang, Xi
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1412.1601
In this paper, we consider the twisted Kähler-Ricci soliton, and show that the existence of twisted Kähler-Ricci soliton with semi-positive twisting form is closely related to the properness of some energy functionals. We also consider the conical Kähler-Ricci soliton, and obtain some existence results. In particular, under some assumptions on the divisor and α-invariant, we get the properness of the modified log K-energy and the existence of conical Kähler-Ricci soliton with suitable cone angle.