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

TL;DR

This paper establishes $L^{ abla}$ and H"older estimates for parabolic complex Monge-Ampere and Hessian equations using PDE techniques, extending previous results to broader classes of equations.

Contribution

The paper generalizes $L^{ abla}$ estimates from complex Monge-Ampere to Hessian equations, providing new bounds for parabolic PDEs in complex geometry.

Findings

Established $L^{ abla}$ estimates for parabolic complex Monge-Ampere equations

Extended $L^{ abla}$ estimates to parabolic Hessian equations

Provided H"older estimates for these classes of 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 H\"older estimates. We also generalize the $L^{\infty}$ estimates to parabolic Hessian equations.