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

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

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Pei-Ken Hung , Columbia University
Fine Hall 314

We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. 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 monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established by Brendle.