Minkowski problem for complete noncompact convex hypersurfaces - Chou, Kai-Seng; Wang, Xu-Jia (Topological Methods in Nonlinear Analysis, 1995)
We present some sufficient conditions on the existence of a complete noncompactconvex hypersurface whose Gauss curvature is equal to a prescribedfunction on the unit sphere. By the Legendre transform this problem is reducedto the solvability of the Monge-Ampère equation subject to certain boundaryconditions.