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\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\Sigma \subset M$$\end{document}Σ⊂Mand mass\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$m\in {\mathbb {R}}$$\end{document}m∈R. If\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$3\le \dim (M)\le 7$$\end{document}3≤dim(M)≤7, (M,g) has non-negative scalar curvature, and the boundary\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\partial M$$\end{document}∂Mis mean-convex, we obtain the Riemannian Penrose-type inequality\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\begin{aligned} m\ge \left( \frac{1}{2}\right) ^{\frac{n}{n-1}}\,\left( \frac{|\Sigma |}{\omega _{n-1}}\right) ^{\frac{n-2}{n-1}} \end{aligned}$$\end{document}m≥12nn-1|Σ|ωn-1n-2n-1as a corollary. Moreover, in the case where\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\partial M$$\end{document}∂Mis 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\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\dim (M)=3$$\end{document}dim(M)=3and\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym} 
				\usepackage{amsfonts} 
				\usepackage{amssymb} 
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\Sigma $$\end{document}Σis a connected free boundary hypersurface.