On stability and the convergence of the kähler-ricci flow

Abstract

Assuming uniform bounds for the curvature, the exponential convergence of the Kähler-Ricci flow is established under two con- ditions which are a form of stability: the Mabuchi energy is bound- ed from below, and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit. © 2006 Journal of Differential Geometry.