Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality

DOI10.1007/s11464-016-0558-3zbMath1353.53045OpenAlexW2516056180MaRDI QIDQ335547

Jie Wu, Chao Xia, Yuxin Ge, Guofang Wang

Publication date: 2 November 2016

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-016-0558-3

zbMATH Keywords

Penrose inequalityAlexandrov-Fenchel inequalityasymptotically hyperbolic manifoldGauss-Bonnet curvatureGauss-Bonnet-Chern (GBC) masspositive mass theorem (PMT)

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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A \(\sigma_2\) Penrose inequality for conformal asymptotically hyperbolic 4-discs ⋮ Chern's magic form and the Gauss-Bonnet-Chern mass ⋮ The Gauss–Bonnet–Chern mass under geometric flows

Cites Work

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• An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality
• Constant mean curvature surfaces in warped product manifolds
• A generalized mass involving higher order symmetric functions of the curvature tensor
• Inverse curvature flows in hyperbolic space
• A new mass for asymptotically flat manifolds
• Rigidity for closed totally umbilical hypersurfaces in space forms
• Integral geometry and geometric inequalities in hyperbolic space
• On Aleksandrov-Fenchel inequalities for \(k\)-convex domains
• Computing asymptotic invariants with the Ricci tensor on asymptotically flat and asymptotically hyperbolic manifolds
• On Witten's proof of the positive energy theorem
• Positive scalar curvature in dim \(\geq 8\)
• Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
• On the Riemannian Penrose inequality in dimensions less than eight
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• On the proof of the positive mass conjecture in general relativity
• Total curvatures of convex hypersurfaces in hyperbolic space
• A positive mass theorem for spaces with asymptotic SUSY compactification
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• The mass of asymptotically hyperbolic manifolds.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Chern's magic form and the Gauss-Bonnet-Chern mass
• A definition of total energy-momenta and the positive mass theorem on asymptotically hyperbolic 3-manifolds. I
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• The mass of spacelike hypersurfaces in asymptotically anti-de Sitter space-times.
• The mass of asymptotically hyperbolic Riemannian manifolds.
• A Penrose inequality for graphs over Kottler space
• Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
• Penrose type inequalities for asymptotically hyperbolic graphs
• A positive mass theorem on asymptotically hyperbolic manifolds with corners along a hypersurface
• A geometric inequality on hypersurface in hyperbolic space
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
• The Gauss-Bonnet-Chern mass for graphic manifolds
• Rigidity and positivity of mass for asymptotically hyperbolic manifolds
• Hyperbolic Alexandrov-Fenchel quermassintegral inequalities. II
• On \(2k\) -minimal submanifolds
• A remarkable property of the Riemann-Christoffel tensor in four dimensions
• Die isoperimetrischen Ungleichungen auf der gewöhnlichen Kugel und für Rotationskörper im \(n\)-dimensionalen sphärischen Raum
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• On the curvatura integra in a Riemannian manifold
• Towards the classification of static vacuum spacetimes with negative cosmological constant
• Evaluation of the ADM mass and center of mass via the Ricci tensor
• Gravitational Energy in Quadratic-Curvature Gravities
• The Gauss–Bonnet–Chern Mass of Conformally Flat Manifolds
• A Class of Critical Riemannian Metrics
• Coordinate Invariance and Energy Expressions in General Relativity
• A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold
• Present status of the Penrose inequality
• The mass of an asymptotically flat manifold
• The Schläfli formula in Einstein manifolds with boundary
• Energy in topologically massive gravity
• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension
• The ADM mass of asymptotically flat hypersurfaces
• Geometric invariance of mass-like asymptotic invariants
• Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs
• Deformation and rigidity results for the 2k‐Ricci tensor and the 2k‐Gauss‐Bonnet curvature
• The equality case of the Penrose inequality for asymptotically flat graphs
• On the center of mass of isolated systems with general asymptotics
• The Einstein Tensor and Its Generalizations
• The GBC mass for asymptotically hyperbolic manifolds