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

2012/09/04 by Simon Brendle, Pei-Ken Hung, Brendle, Simon +5 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematics and Applications #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.1209.0669

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

openalex publication_date 2012/09/04 · arxiv created 2014/07/21 · arxiv updated 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

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• A geometric inequality on hypersurface in hyperbolic space
• The Gauss–Bonnet–Chern mass for graphic manifolds

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