Hypersurfaces of Prescribed Gauss Curvature in Exterior Domains

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.Comment: 15 pages, LaTeX (published version

Mean curvature flow without singularities

We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying graphical mean curvature flow with one additional dimension.Comment: 19 pages, 4 figure