We then prove that a domain of dependence D contains a convex Cauchy surface with principal curvatures bounded from below by a positive constant if and only if the corresponding function φ is in the Zygmund class. Moreover in this case the surface of constant curvature K contained in D has bounded principal curvatures, for every a8723f12c207366643b9f77f38e0" title="Click to view the MathML source">K<0. In this way we get a full classification of isometric immersions of the hyperbolic plane in Minkowski space with bounded shape operator in terms of Zygmund functions of 90dac9de45eec8af3c672e0dd0f221a4" title="Click to view the MathML source">∂D.
Finally, we prove that every domain of dependence as in the hypothesis of the Minkowski problem is foliated by the surfaces of constant curvature K, as K varies in b9a5a8544410f1045889e50e0913ee" title="Click to view the MathML source">(−∞,0).