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

Abstract

In this paper, we develop a series of general integral formulae for compact spacelike hypersurfaces with hyperplanar boundary in the ( n+1)-dimensional Minkowski space–time L n+1 . As an application of them, we prove that the only compact spacelike hypersurfaces in L n+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].