Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality.

Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces ( M ,  g ) with horizon boundary Σ ⊂ M and mass m ∈ R . If 3 ≤ dim ( M ) ≤ 7 , ( M ,  g ) has non-negative scalar curvature, and the boundary ∂ M is mean-convex, we obtain the Riemannian Penrose-type inequality m ≥ 1 2 n n - 1 | Σ | ω n - 1 n - 2 n - 1 as a corollary. Moreover, in the case where ∂ M is not totally geodesic, we show how to construct local perturbations of ( M ,  g ) that increase the scalar curvature. As a consequence, we show that equality holds in the above inequality if and only if the exterior region of ( M ,  g ) is isometric to a Schwarzschild half-space. Previously, these results were only known in the case where dim ( M ) = 3 and Σ is a connected free boundary hypersurface.