A comparison principle for parabolic complex Monge-Ampère equations

Abstract

In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Ampère equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for Parabolic complex Monge-Ampère equations and use it to study the existence and uniqueness of viscosity solution in certain cases where the sets $\{z\in \Omega :f(t,z)=0\}$ may be pairwise disjoint.

15 pages. In the first version, there is an error in the proof of Lemma 3.3. In the second version, we add some conditions on $\Phi$ and $f$ under which our method works