Existence of entire solutions to the Monge-Ampère equation

We prove the existence of infinitely many entire convex solutions to the Monge-Ampère equation det D²u = f in ℝⁿ, assuming that the inhomogeneous term f ≥ 0 and is of polynomial growth at infinity. When f satisfies the doubling condition, we show that solution is of polynomial growth. As an application, we resolve the existence of translating solutions to a class of Gauss curvature flow.