A sharp height estimate for compact spacelike hypersurfaces with constant r-mean curvature in the Lorentz–Minkowski space and application

In this paper we obtain a sharp height estimate concerning compact spacelike hypersurfaces ΣnΣn immersed in the (n+1)(n+1)-dimensional Lorentz–Minkowski space Ln+1Ln+1 with some nonzero constant r  -mean curvature, and whose boundary is contained into a spacelike hyperplane of Ln+1Ln+1. Furthermore, we apply our estimate to describe the nature of the end of a complete spacelike hypersurface of Ln+1Ln+1.