A second order estimate for general complex Hessian equations

TL;DR

This paper develops second order a priori estimates for solutions to complex Hessian equations with gradient-dependent right-hand sides, advancing the understanding of their regularity properties.

Contribution

It provides new second order estimates for complex Hessian equations with gradient-dependent terms, extending previous regularity results.

Findings

Established $C^2$ estimates for solutions

Handled gradient-dependent right-hand sides

Enhanced regularity theory for complex Hessian equations

Abstract

We derive a priori $C^2$ estimates for the $\chi$-plurisubharmonic solutions of general complex Hessian equations with right-hand side depending on gradients.