LONGTIME EXISTENCE OF THE KAHLER-RICCI FLOW ON Cn

We produce longtime solutions to the Kahler-Ricci flow for complete Kahler metrics on C-n without assuming the initial metric has bounded curvature, thus extending results in an earlier work of the authors. We prove the existence of a longtime bounded curvature solution emerging from any complete U(n)-invariant Kahler metric with non-negative holomorphic bisectional curvature, and that the solution converges as t ->infinity to the standard Euclidean metric after rescaling. We also prove longtime existence results for more general Kahler metrics on C-n which are not necessarily U(n)-invariant.