The equality case of the Penrose inequality for asymptotically flat graphs

DOI10.1090/S0002-9947-2014-06090-XzbMath1376.53062arXiv1205.2061OpenAlexW2964296521MaRDI QIDQ5496574

Damin Wu, Lan-Hsuan Huang

Publication date: 2 February 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.2061

zbMATH Keywords

Schwarzschild solutionstrong maximum principleminimal boundarygraphical hypersurfacelinearized scalar curvature operator

Mathematics Subject Classification ID

General relativity (83C99) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24)

Related Items (21)

Conformal modulus and its reduction via mean curvatures ⋮ An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality ⋮ Penrose-type inequalities with a Euclidean background ⋮ Entropy flux - electrostatic capacity - graphical mass ⋮ Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality ⋮ Extrinsic black hole uniqueness in pure Lovelock gravity ⋮ Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass ⋮ Doubling of asymptotically flat half-spaces and the Riemannian Penrose inequality ⋮ A Penrose type inequality for graphs over Reissner-Nordström-anti-deSitter manifold ⋮ A new mass for asymptotically flat manifolds ⋮ The Gauss-Bonnet-Chern mass of higher-codimension graphs ⋮ The GBC mass for asymptotically hyperbolic manifolds ⋮ The Gauss-Bonnet-Chern mass for graphic manifolds ⋮ Deforming the scalar curvature of the de Sitter-Schwarzschild space ⋮ A Penrose inequality for graphs over Kottler space ⋮ Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ On the stability of the positive mass theorem for asymptotically hyperbolic graphs ⋮ Penrose inequalities and a positive mass theorem for charged black holes in higher dimensions ⋮ Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

Cites Work

• Unnamed Item
• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Hypersurfaces with nonnegative scalar curvature
• On the Riemannian Penrose inequality in dimensions less than eight
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Geometric inequalities and rigidity theorems on equatorial spheres
• Superharmonic functions in \(\mathbb{R}^n\) and the Penrose inequality in general relativity
• Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
• Penrose type inequalities for asymptotically hyperbolic graphs
• A volumetric Penrose inequality for conformally flat manifolds
• On the Hessian of a function and the curvature of its graph
• RADIATION FROM A RINDLER-DIRAC ELECTRON
• The mass of an asymptotically flat manifold
• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension
• Two-ended hypersurfaces with zero scalar curvature
• The ADM mass of asymptotically flat hypersurfaces
• Mass-Capacity Inequalities for Conformally Flat Manifolds with Boundary
• On Hypersurfaces with no Negative Sectional Curvatures
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

This page was built for publication: The equality case of the Penrose inequality for asymptotically flat graphs