Kähler-Ricci solitons on toric Fano varieties

In this paper, we discuss the existence of Kähler-Ricci soliton by reducing to solve certain complex Monge-Amp\'ere equation on a compact complex manifold with positive first Chern class, especially on a toric Fano variety. As similar as the study of Kähler-Einstein metrics, one can use continuity method to solve such a complex Monge-Amp\'ere equation. In fact, many places can be modified as in the proof of uniqueness ([TZ2) although some new difficulties will arise. The purpose of this paper is to give an approach to solve those difficulties.