Abstract

In this paper, we consider prescribed shifted Gauss curvatures equations for horo-convex hypersurfaces in $${\mathbb {H}}^{n+1}$$ . Under some sufficient conditions, we obtain an existence result by the standard degree theory based on the a priori estimates for solutions to the equations. Different from the prescribed Weingarten curvatures problem in space forms, we do not impose a sign condition for the radial derivative of the functions in the right-hand side of the equations to prove the existence due to the horo-covexity of hypersurfaces in $${\mathbb {H}}^{n+1}$$ .

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