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

A class of Hessian quotient equations in the warped product manifold