| We prove Cinfinity convergence for suitably normalized solutions of the parabolic complex Monge-Ampere equation on compact Hermitian manifolds. This provides a parabolic proof of a recent result of Tosatti-Weinkove.;Additionally, let X = M x E where M is an m-dimensional Kahler manifold with negative first Chern class and E is an n-dimensional complex torus. We obtain C infinity convergence of the normalized Kahler-Ricci flow on X to a Kahler-Einstein metric on M. This strengthens a convergence result of Song-Weinkove and confirms their conjecture. |
