Spacelike hypersurfaces of constant mean curvature with free boundary in Lorentzian space forms

Abstract

In this paper we introduce a variational problem for spacelike hypersurfaces in Lorentzian space forms whose critical points turn out to be constant mean curvature spacelike hypersurfaces which intersect a given support hypersurface at a constant hyperbolic angle. For the two-dimensional case, when the support surface is totally umbilical we prove that only such surfaces are totally umbilical too.