Viscosity solutions to parabolic complex Monge-Ampère equations

In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Ampère equations on a strongly pseudoconvex domain by the viscosity method. We extend the results in [EGZ15b] on the existence of solution and the convergence at infinity. We also establish the Hölder regularity of the solutions when the Cauchy-Dirichlet data are Hölder continuous.