Near-equality of the Penrose inequality for rotationally symmetric Riemannian manifolds

DOI10.1007/s00023-012-0172-1zbMath1260.83111arXiv1109.2165OpenAlexW3098468262WikidataQ115389947 ScholiaQ115389947MaRDI QIDQ1937033

Christina Sormani, Dan A. Lee

Publication date: 11 February 2013

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

Full work available at URL: https://arxiv.org/abs/1109.2165

zbMATH Keywords

positive mass theoremSchwarzschild spacePenrose inequalityLipschitz distance

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Black holes (83C57) Applications of differential geometry to physics (53Z05) Gravitational energy and conservation laws; groups of motions (83C40) Approximation procedures, weak fields in general relativity and gravitational theory (83C25)

Related Items

Stability of the PMT and RPI for asymptotically hyperbolic manifolds foliated by IMCF ⋮ Metrics with \(\lambda_1(-\Delta + k R) \ge 0\) and flexibility in the Riemannian Penrose inequality ⋮ Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass ⋮ Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry ⋮ Analysis, geometry and topology of positive scalar curvature metrics. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting) ⋮ Properties of the Intrinsic Flat Distance ⋮ 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 ⋮ The nonlinear stability of rotationally symmetric spaces with low regularity ⋮ Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ On the stability of the positive mass theorem for asymptotically hyperbolic graphs ⋮ Sequences of three dimensional manifolds with positive scalar curvature ⋮ The positive mass theorem for manifolds with distributional curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Smooth convergence away from singular sets
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• A level set analysis of the Witten spinor with applications to curvature estimates
• On the near-equality case of the positive mass theorem
• On the Riemannian Penrose inequality in dimensions less than eight
• On the proof of the positive mass conjecture in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A new proof of the positive energy theorem.
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Curvature estimates in asymptotically flat manifolds of positive scalar curvature
• Curvature estimates and the positive mass theorem
• Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
• Coordinate Invariance and Energy Expressions in General Relativity
• The mass of an asymptotically flat manifold
• A note on asymptotically flat metrics on ℝ³ which are scalar-flat and admit minimal spheres
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Currents in metric spaces