Addendum to ``Spacelike hypersurfaces with constant higher order mean curvature in the Minkowski space-time'' (Q1602450)

Two of the authors developed in [\textit{L. J. Alías} and \textit{J. M. Malacarne}, ibid. 41, No. 4, 359-375 (2002; Zbl 1013.53035)] a series of integral formulas for compact spacelike hypersurfaces in \((n+1)\)-dimensional Minkowski space-time. Here the following theorem and its proof are added to that paper. Assume that two mean curvatures \(H_k\) and \(H_1\) of a compact spacelike hypersurface \(M\) with spherical boundary in Minkowski space-time are proportional: \(H_k= cH_1\), \(c=\text{const}\). Then \(M\) is either a hyperplanar ball or a hyperbolic cap.