We prove an existence theorem for convex hypersurfaces of prescribed Gauß curvature in the complement of a compact set in Euclidean space which are close to a cone.
This paper has appeared in "Calc. Var. Partial Differential Equations". Springer-Verlag is the copyright holder of this article. The original publication is available on LINK at http://link.springer.de, more precisely, see http://dx.doi.org/10.1007/s005260100118.