The Kähler Ricci flow around complete bounded curvature Kähler metrics

Abstract

We produce complete bounded curvature solutions to Kähler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain related flow results for non-smooth as well as degenerate initial conditions. We also obtain a stability result for complex space forms under the flow.

22 pages; editions made to earlier version (including revision of title, addition to Theorem 1.2 and correction in proof of Claim 2.2)