Uniformly strong convergence of K\"ahler-Ricci flows on a Fano manifold

Abstract

In this paper, we study the uniformly strong convergence of K\"ahler-Ricci flow on a Fano manifold with varied initial metrics and smooth deformation complex structures. As an application, we prove the uniqueness of K\"ahler-Ricci solitons in sense of diffeomorphism orbits. The result generalizes Tian-Zhu's theorem for the uniqueness of of K\"ahler-Ricci solitons on a compact complex manifold, and it is also a generalization of Chen-Sun's result of for the uniqueness of of K\"ahler-Einstein metric orbits.