  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).
