On the near-equality case of the positive mass theorem

DOI10.1215/00127094-2009-021zbMath1168.53018arXiv0705.0677OpenAlexW2963735083MaRDI QIDQ1018556

Dan A. Lee

Publication date: 20 May 2009

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.0677

zbMATH Keywords

scalar curvaturecomplete asymptotically flat manifoldpositive mass conjecture

Mathematics Subject Classification ID

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

Related Items (13)

Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Asymptotically hyperbolic manifolds with small mass ⋮ Stability of the PMT and RPI for asymptotically hyperbolic manifolds foliated by IMCF ⋮ Near-equality of the Penrose inequality for rotationally symmetric Riemannian manifolds ⋮ Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry ⋮ IMCF and the stability of the PMT and RPI under \(L^2\) convergence ⋮ Sobolev stability of the positive mass theorem and Riemannian Penrose inequality using inverse mean curvature flow ⋮ Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ On the stability of the positive mass theorem for asymptotically hyperbolic graphs ⋮ The \(p\)-harmonic capacity of an asymptotically flat 3-manifold with non-negative scalar curvature ⋮ On the Riemannian Penrose inequality in dimensions less than eight ⋮ Stability of the positive mass theorem for axisymmetric manifolds ⋮ Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space

Cites Work

• Unnamed Item
• A level set analysis of the Witten spinor with applications to curvature estimates
• On the Riemannian Penrose inequality in dimensions less than eight
• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Coordinate Invariance and Energy Expressions in General Relativity
• The mass of an asymptotically flat manifold

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