Exterior Dirichlet Problem for Translating Solutions of Gauss Curvature Flow in Minkowski Space

Abstract

We prove the existence of solutions to a class of Monge-Ampère equations on exterior domains in ${ℝ}^n(n\ge 2)$ and the solutions are close to a cone. This problem comes from the study of the flow by powers of Gauss curvature in Minkowski space.