Second order estimates for equations with sums of Hessian operators on Hermitian manifolds

TL;DR

This paper derives second-order a priori estimates for solutions to complex Hessian equations on Hermitian manifolds, advancing the understanding of these nonlinear PDEs with geometric significance.

Contribution

It introduces a new concavity inequality for sum-of-Hessian operators, enabling second-order estimates for complex Hessian equations on Hermitian manifolds.

Findings

Established second-order a priori estimates for solutions.

Developed a concavity inequality for sum-of-Hessian operators.

Extended techniques to compact Hermitian manifolds.

Abstract

In this paper, we establish an a priori second-order estimate for admissible solutions satisfying a dynamic plurisubharmonic condition to equations involving sums of Hessian operators on compact Hermitian manifolds. The estimate is derived using a concavity inequality for complex sum-of-Hessian operators.