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 .
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