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We prove existence in the Minkowski space of entire spacelike hypersurfaceswith constant negative scalar curvature and given set of lightlike directionsat infinity; we also construct the entire scalar curvature flow with prescribedset of lightlike directions at infinity, and prove that the flow converges to aspacelike hypersurface with constant scalar curvature. The proofs rely onbarriers construction and a priori estimates.

Entire scalar curvature flow and hypersurfaces of constant scalar curvature in Minkowski space