Area Maximizing Surfaces in Lorentzian Spaces

Abstract

In this paper we provide new results for area maximizing compact spacelike surfaces with boundary embedded in Lorentz-Minkowski space, as well as establish the uniqueness of the Dirichlet problem for maximal graphs in the aforementioned space. Moreover, we extend our results to more general Lorentzian spaces that admit an in nitesimal timelike symmetry.