Constant mean curvature spacelike hypersurfaces with spherical boundary in the Lorentz-Minkowski space

Abstract

We study compact spacelike hypersurfaces (necessarily with non-empty boundary) with constant mean curvature in the ( n + 1)-dimensional Lorentz-Minkowski space. In particular, when the boundary is a round sphere we prove that the only such hypersurfaces are the hyperplanar round balls (with zero mean curvature) and the hyperbolic caps (with non-zero constant mean curvature).