Curvature estimates for a class of Hessian quotient type curvature equations

In this paper, we are concerned with the hypersurface that can be locally represented as a graph and satisfies a class of Hessian quotient type curvature equations. We establish interior curvature estimates under the condition of 0 <= l<k <= Cn-1p-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le l<k\le C_{n-1}<^>{p-1}$$\end{document}. As an application, we prove Bernstein type theorem for this type curvature equation. We also focus on closed star shaped hypersurface satisfying this type curvature equation and obtain the global curvature estimation.