Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics

Abstract

We prove that constant scalar curvature Kähler metric "adjacent" to a fixed Kähler class is unique up to isomorphism.The proof is based on the study of a fourth order evolution equation, namely, the Calabi flow, from a new geometric perspective, and on the geometry of the space of Kähler metrics.