Weak solutions to mean curvature flow respecting obstacles I: the graphical case

We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach of M. Saez and the second author yields a global weak solution to the original problem for general initial data and onesided obstacles.Comment: updated version with minor corrections and 2 new figure

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