The nonlinear stability of rotationally symmetric spaces with low regularity

DOI10.1016/j.jfa.2014.12.012zbMath1316.53058arXiv1401.6192OpenAlexW2963103190MaRDI QIDQ2261954

Christina Sormani, Philippe G. LeFloch

Publication date: 13 March 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6192

zbMATH Keywords

geometric analysisintegral currentscompactness theoremHawking massADM-massflat convergence\(L^2_{\mathrm{loc}}\)-regularityrotationally symmetric space

Mathematics Subject Classification ID

Integral geometry (53C65) Differential geometry of symmetric spaces (53C35) Currents in global analysis (58A25)

Related Items (17)

Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Stability of the PMT and RPI for asymptotically hyperbolic manifolds foliated by IMCF ⋮ The Yamabe problem for distributional curvature ⋮ Weak scalar curvature lower bounds along Ricci flow ⋮ ADM mass for \(C^0\) metrics and distortion under Ricci-DeTurck flow ⋮ Sewing Riemannian manifolds with positive scalar curvature ⋮ 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 ⋮ Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Stability of the spacetime positive mass theorem in spherical symmetry ⋮ Sequences of three dimensional manifolds with positive scalar curvature ⋮ Lower semicontinuity of ADM mass under intrinsic flat convergence ⋮ Stability of the positive mass theorem for axisymmetric manifolds ⋮ Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces ⋮ Singularity scattering laws for bouncing cosmologies: a brief overview ⋮ The positive mass theorem for manifolds with distributional curvature

Cites Work

• Smooth convergence away from singular sets
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\)
• Weak convergence of currents and cancellation
• On the proof of the positive mass conjecture in general relativity
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Definition and weak stability of nonconservative products
• Near-equality of the Penrose inequality for rotationally symmetric Riemannian manifolds
• Shock waves and gravitational waves in matter spacetimes with Gowdy symmetry
• Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
• Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
• Definition and stability of Lorentzian manifolds with distributional curvature
• Normal and integral currents
• Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• 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
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