Convergence of K\"ahler-Ricci flow on lower dimensional algebraic manifolds of general type

Abstract

In this paper, we prove that the $L^4$-norm of Ricci curvature is uniformly bounded along a K\"ahler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold $M$ of general type and with dimension $n\le 3$, any solution of the normalized K\"ahler-Ricci flow converges to the unique singular K\"ahler-Einstein metric on the canonical model of $M$ in the Cheeger-Gromov topology.