Fully non-linear elliptic equations on compact almost Hermitian manifolds

TL;DR

This paper develops a priori estimates for fully non-linear elliptic equations on compact almost Hermitian manifolds and applies these results to solve complex Hessian and Monge-Ampère equations in this setting.

Contribution

It introduces new a priori estimates and solves complex Hessian and Monge-Ampère equations on almost Hermitian manifolds, extending classical results to a broader geometric context.

Findings

Established a priori estimates for non-linear equations on almost Hermitian manifolds

Solved complex Hessian and Monge-Ampère equations in the almost Hermitian setting

Extended classical complex geometric PDE results to non-integrable structures

Abstract

In this paper, we establish a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we solve the complex Hessian equation and the Monge--Amp\`ere equation for $(n-1)$-plurisubharmonic equations in the almost Hermitian setting.