The last decades have seen a steadily growing interest in the study of a priori estimates of the height function of constant mean curvature compact graphs or, more generally, compact hypersurfaces with boundary having some constant higher order mean curvature immersed into semi-Riemannian product spaces of the type \(\mathbb {R}\times M^n\) or \(-\mathbb {R}\times M^n\) , where \(M^n\) is an arbitrary Riemannian manifold.