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

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 Mon-zero constant mean curvature). (C) 1998 Elsevier Science B.V. All rights reserved.