A Minkowski inequality for hypersurfaces in the anti-de Sitter-Schwarzschild manifold. (English) Zbl 1331.53078
Summary: We prove a sharp inequality for hypersurfaces in the \(n\)-dimensional anti-de Sitter-Schwarzschild manifold for general \(n \geq 3\). 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 [Publ. Math., Inst. Hautes Étud. Sci. 117, 247–269 (2013; Zbl 1273.53052)].
MSC:
| 53C40 | Global submanifolds |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
Citations:
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