Penrose type inequalities for asymptotically hyperbolic graphs

DOI10.1007/s00023-012-0218-4zbMath1269.83068arXiv1201.3321OpenAlexW3098682805MaRDI QIDQ2377319

Anna Sakovich, Mattias Dahl, Romain Gicquaud

Publication date: 28 June 2013

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3321

zbMATH Keywords

graphsasymptotically hyperbolic manifoldanti-de Sitter Schwarzschild metricPenrose type inequalities

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Black holes (83C57) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05)

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Cites Work

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• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• On the Riemannian Penrose inequality in dimensions less than eight
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• The area of horizons and the trapped region
• Remarks on Sobolev inequalities and stability of minimal submanifolds
• Total curvatures of convex hypersurfaces in hyperbolic space
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Elliptic partial differential equations of second order
• The mass of asymptotically hyperbolic manifolds.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• The mass of asymptotically hyperbolic Riemannian manifolds.
• Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
• A volumetric Penrose inequality for conformally flat manifolds
• Rigidity and positivity of mass for asymptotically hyperbolic manifolds
• Present status of the Penrose inequality
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• A remark on the Sobolev inequality for Riemannian submanifolds
• The ADM mass of asymptotically flat hypersurfaces
• The measure of the critical values of differentiable maps

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