A Minkowski Inequality for Hypersurfaces in the Anti-de Sitter-Schwarzschild Manifold

We prove a sharp inequality for hypersurfaces in the n-dimensional anti-de Sitter-Schwarzschild manifold for general n≥3. This inequality generalizes the classical Minkowski inequality for surfaces in the three-dimensional euclidean space and has a natural interpretation in terms of the Penrose inequality for collapsing null shells of dust. The proof relies on a new monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by the first author in [3].