Entire hypersurfaces of constant scalar curvature in Minkowski space

We show that every regular domain D in Minkowski space ℝn,1 which is not a wedge admits an entire hypersurface whose domain of dependence is D and whose scalar curvature is a prescribed constant (or function, under suitable hypotheses) in (- ∞, 0). Under rather general assumptions, these hypersurfaces are unique and provide foliations of D. As an application, we show that every maximal globally hyperbolic Cauchy compact flat spacetime admits a foliation by hypersurfaces of constant scalar curvature, generalizing to any dimension previous results of Barbot-Béguin-Zeghib (for n = 2) and Smith (for n = 3).