Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems

DOI10.1007/s10455-012-9343-zzbMath1268.53076arXiv1201.4249OpenAlexW3104157021MaRDI QIDQ1942005

James D. E. Grant, Jan-Hendrik Treude

Publication date: 25 March 2013

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4249

zbMATH Keywords

Lorentzian manifoldsarea and volume comparison theoremsHawking's singularity theorems

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Space-time singularities, cosmic censorship, etc. (83C75) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Classical or axiomatic geometry and physics (51P05)

Related Items

The Hawking-Penrose singularity theorem for \(C^{1,1}\)-Lorentzian metrics ⋮ A review of Lorentzian synthetic theory of timelike Ricci curvature bounds ⋮ A note on null distance and causality encoding ^* ⋮ Achronal limits, Lorentzian spheres, and splitting ⋮ Volume comparison for \(\mathcal {C}^{1,1}\)-metrics ⋮ Lorentzian Gromov-Hausdorff theory and finiteness results ⋮ Lorentzian area and volume estimates for integral mean curvature bounds ⋮ Hawking's singularity theorem under a bounded integral norm of Ricci curvature

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