On a class of fully nonlinear elliptic equations on closed Hermitian manifolds

TL;DR

This paper investigates a class of fully nonlinear elliptic equations on closed Hermitian manifolds, establishing smooth a priori estimates and proving the existence of solutions using a novel Hermitian metric and the continuity method.

Contribution

The paper introduces a new Hermitian metric and applies the continuity method to prove existence results for fully nonlinear elliptic equations on Hermitian manifolds.

Findings

Established $C^ abla$ estimates for solutions.

Proved existence of admissible solutions.

Constructed a new Hermitian metric for the analysis.

Abstract

We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch the method of continuity.