Fano Manifolds with Weak almost Kahler-Ricci Solitons

In this paper, we prove that a sequence of weak almost Kahler-Ricci solitons under further suitable conditions converges to a Kahler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology. As a corollary, we show that on a Fano manifold with the modified K-energy bounded below, there exists a sequence of weak almost Kahler-Ricci solitons which converges to a Kahler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology.