Inspired by the canonical neighborhood theorem of G. Perelman in 3 dimensional, we study the weak compactness of sequence of ricci flow with scalar curvature bound, Kappa non-collapsing and integral curvature bound.

All of these constraints are natural in the Kahler ricci flow in Fano surface and as an application, we give a ricci flow based proof to the Calabi conjecture in Fano surface.