A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

TL;DR

This paper extends the theory of fully non-linear elliptic equations to compact almost Hermitian manifolds, establishing existence results and solving specific complex equations in this generalized setting.

Contribution

It generalizes the sub-slope concept to almost Hermitian manifolds and proves existence of solutions for a broad class of non-linear equations, including complex Hessian quotient and deformed Hermitian-Yang-Mills equations.

Findings

Established existence of solutions for non-linear equations on almost Hermitian manifolds.

Solved the complex Hessian quotient equation in the almost Hermitian setting.

Addressed the deformed Hermitian-Yang-Mills equation on compact almost Hermitian manifolds.

Abstract

In this paper, we generalize the definition of sub-slope, introduced by Guo-Song, to almost Hermitian manifolds and prove the existence of solutions for a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we solve the complex Hessian quotient equation and the deformed Hermitian-Yang-Mills equation in the almost Hermitian setting.