The evolution of convex surfaces by powers of the Gauss curvature is a fully nonlinear parabolic equation. In particular, its translating solitons are complete convex graphs of solutions to a Monge-Ampere type equation. Hence, the classification of translators is a Liouville type theory for a Monge- Ampere type equation. In this talk, we address the existence and classification of translating surfaces by sub-affine-critical powers of the Gauss curvature.