We prove the existence of solutions to a class of Monge-Ampère equations on exterior domains in 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.
"Exterior Dirichlet Problem for Translating Solutions of Gauss Curvature Flow in Minkowski Space." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/671537