Monge-Ampère equations with right-hand sides of polynomial growth

We study the regularity and the growth rates of solutions to two-dimensional Monge-Ampère equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow.