On a Class of Fully Nonlinear Elliptic Equations on Closed Hermitian Manifolds

We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive C∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^\infty $$\end{document} a priori estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metric is constructed to launch the method of continuity.