Résume  The Riemannian Penrose inequality is a fundamental result in mathematical general relativity and provides an estimate for the area of an outermost minimal surface in an asymptotically flat threemanifold solely in terms of the global mass. It was originally proven by Huisken and Illmanen using a weak version of the inverse mean curvature flow which has the crucial property of evolving the socalled Hawking mass in a nondecreasing way. In this talk, I will present a recent result which shows that a suitable version of the Penrose inequality continues to hold if the ambient manifold has a noncompact boundary. The main ingredient in the proof is a free boundary version of the weak inverse mean curvature flow which is obtained as the limit of a new approximation scheme accommodating for the presence of the noncompact boundary.
