EXISTENCE OF ENTIRE SOLUTIONS TO THE MONGE-AMPERE EQUATION

Abstract. We prove the existence of infinitely many entire convex solutions to the Monge-Ampère equation detD2u = 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. 1