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 conditions which are a form of stability: the Mabuchi energy is bounded 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.

18 pages, no figure