Existence for translating solutions of Gauss curvature flow on exterior domains

In this paper, we use the Perron method to prove the existence of viscosity solutions to a class of Monge–Ampère equations on exterior domains in Rn(n≥2)Rn(n≥2) with prescribed asymptotic behavior at infinity. This problem comes from the study of Gauss curvature flow and its generalization, the flow by powers of Gauss curvature.