Degenerate complex Hessian equations on compact Hermitian manifolds

TL;DR

This paper establishes uniform a priori estimates for solutions to degenerate complex Hessian equations on compact Hermitian manifolds, extending previous results and offering a new proof approach.

Contribution

It provides a novel uniform a priori estimate method for degenerate complex Hessian equations on Hermitian manifolds, building on Monge-Ampère equation techniques.

Findings

Extended existing estimates to degenerate Hessian equations

Provided an alternative proof method

Connected results to Monge-Ampère equations

Abstract

In this note we provide uniform a priori estimates for solutions to degenerate complex Hessian equations on compact hermitian manifolds. Our approach relies on the corresponding a priori estimates for Monge-Amp\`ere equations; it provides an extension as well as a short alternative proof to results of Dinew-Ko{\l}odziej, Ko{\l}odziej-Nguyen and Guo-Phong-Tong.