A new parabolic flow in Kaehler manifolds

Abstract

In this paper, we introduce a new parabolic equation on K\"ahler manifolds. The static point of this flow is related to the existence of a lower bound of the Mabuchi energy. In this paper, we prove the flow always exists for all times for any initial smooth data. Further more, if the initial metric has non-negative bisectional curvature, we prove the flow converges to a static metric eventually.