A class of Hessian quotient equations in the warped product manifold.

In this paper, we consider a class of Hessian quotient equations in the warped product manifold $\overline{M}=I\times_{\lambda}M$. Under some sufficient conditions, we obtain an existence result for the star-shaped compact hypersurface $\Sigma$ in $\overline{M}$ using standard degree theory based on a priori estimates for solutions to the Hessian quotient equations.