A comparison principle for parabolic complex Monge-Ampère equations

Abstract: In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Amp`ere equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for Parabolic complex Monge-Amp`ere 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.