Spacelike surfaces of constant mean curvature with free boundary in the Minkowski space

Abstract

In this paper we introduce a variational problem for spacelike surfaces in the Minkowski space whose critical points turn out to be constant mean curvature spacelike surfaces which intersect a given support surface at a constant hyperbolic angle. In the case where the support surface is either a spacelike 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 discussions on this variational problem for the general n-dimensional case.