Spacelike hypersurfaces with constant higher order mean curvature in Minkowski space-time

In this paper, we develop a series of general integral formulae for compact spacelike hyper-surfaces with hyperplanar boundary in the (n + I)-dimensional Minkowski space-time Ln+1. As an application of them, we prove that the only compact spacelike hypersurfaces in Ln+1 having constant higher order mean curvature and spherical boundary are the hyperplanar balls (with zero higher order mean curvature) and the hyperbolic caps (with nonzero constant higher order mean curvature). This extends previous results obtained by the first author, jointly with Pastor, for the case of constant mean curvature [J. Geom. Phys. 28 (1998) 85] and the case of constant scalar curvature [Ann. Global Anal. Geom. 18 (2000) 75]. (C) 2002 Elsevier Science B.V. All rights reserved.