Twisted and conical Kähler-Ricci soliton on Fano manifolds

Abstract

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 $\alpha$-invariant, we get the properness of the modified log K-energy and the existence of conical Kähler-Ricci soliton with suitable cone angle.

References in corpus (4)

• K-stability and Kähler-Einstein metrics
• Existence of Gradient Kahler-Ricci Solitons
• Conical Kahler-Einstein metric revisited
• Modified Futaki invariant and equivariant Riemann-Roch formula