K\"ahler Ricci flow on Fano surfaces (I)

Abstract

We show the properties of the blowup limits of \KRf solutions on Fano surfaces if Riemannian curvature is unbounded. As an application, on every toric Fano surface, we prove that \KRf converges to a K\"ahler Ricci soliton metric if the initial metric has toric symmetry. Therefore we give a new Ricci flow proof of existence of K\"ahler Ricci soliton metrics on toric surfaces.