The $L^{\infty }$ estimates for parabolic complex Monge-Ampere and Hessian equations

Abstract

In this paper, we consider a version of parabolic complex Monge-Ampere equations, and use a PDE approach similar to Phong et al to establish $L^{\infty }$ and Hölder estimates. We also generalize the $L^{\infty }$ estimates to parabolic Hessian equations.