Lj. Alias et Ja. Pastor, Spacelike surfaces of constant mean curvature with free boundary in the Minkowski space, CLASS QUANT, 16(4), 1999, pp. 1323-1331
In this paper we introduce a variational problem for spacelike surfaces in
the Minkowski space whose critical points turn out to be constant mean curv
ature spacelike surfaces which intersect a given support surface at a const
ant hyperbolic angle. In the case where the support surface is either a spa
celike plane or a hyperbolic plane we prove that the only such surfaces are
the planar discs (with zero mean curvature) and the hyperbolic caps (with
non-zero constant mean curvature). We also include some additional discussi
ons on this variational problem for the general n-dimensional case.