Sharp height estimate in Lorentz-Minkowski space revisited

Abstract

In this paper, we deal with compact (necessarily with nonempty boundary) generalized linear Weingarten spacelike hypersurfaces immersed into the Lorentz-Minkowski space $\mathbb L^{n+1}$, which means that there exists a linear relation involving some of the corresponding higher order mean curvatures. In this setting, we obtain a sharp height estimate concerning such a hypersurfaces whose boundary is contained in a spacelike hyperplane of $\mathbb L^{n+1}$. Furthermore, we apply our estimate to describe the nature of the end of a complete generalized linear Weingarten spacelike hypersurface in $\mathbb L^{n+1}$.