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

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 $L^{\mathrm{\infty }}$ and H"older estimates. We also generalize the $L^{\mathrm{\infty }}$ estimates to parabolic Hessian equations.