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 \(0\le l<k\le C_{n-1}^{p-1}\) $0\le l<k\le C_{n-1}^{p-1}$ . 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.