A rigidity result for the graph case of the Penrose inequality
  In this note we prove a global rigidity result for asymptotically flat, scalar flat Euclidean hypersurfaces with a minimal horizon lying in a hyperplane, under a natural ellipticity condition. As a consequence we obtain, in the context of the Riemannian Penrose conjecture, a local rigidity result for the family of exterior Schwarzschild solutions (viewed as graphs in Euclidean space). 
Levi Lopes de Lima, Frederico Gir\~ao
math.DG gr-qc