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

Abstract

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