A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold

Abstract

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 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].

19 pages. The paper has been accepted for publication in CPAM

References in corpus (1)

• A Gibbons-Penrose inequality for surfaces in Schwarzschild spacetime

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