Entire downward solitons to the scalar curvature flow in Minkowski space

Existence and uniqueness in Minkowski space of entire downward translating solitons with prescribed values at infinity for a scalar curvature flow equation. The radial case translates into an ordinary differential equation and the general case into a fully non-linear elliptic PDE on R^n.
Comment: 26 pages, to appear in Annales de l'Institut Henri Poincar\'e, Analyse Non Lin\'eaire