Local gradient estimates for a type of fully nonlinear equations

Assuming that the solution is bounded from one-side, by Bernstein-type arguments, on (M2,g),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M<^>{2},g),$$\end{document} we prove the local gradient estimates for a type of fully nonlinear equation from conformal geometry.