On convergence of the Kahler—Ricci flow

摘要

We study the convergence of the Kahler—Ricci flow on a Fano manifold under some stability conditions. More precisely we assume that the first eingenvalue of the θ-operator acting on vector fields is uniformly bounded along the flow, and in addition the Mabuchi energy decays at most logarithmically. We then give different situations in which the condition on the Mabuchi energy holds.