Volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci curvature bounds

DOI10.1007/s10714-010-1106-1zbMath1222.83159OpenAlexW1994418669MaRDI QIDQ637619

Seong-Hun Paeng

Publication date: 6 September 2011

Published in: General Relativity and Gravitation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10714-010-1106-1

zbMATH Keywords

Lorentzian manifoldspacelike hypersurface(weighted) volume comparisongeneralized Ricci tensorintegral Ricci curvature bound

Mathematics Subject Classification ID

Geometrodynamics and the holographic principle (83E05) Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05)

Related Items (2)

Volumes and intrinsic diameters of hypersurfaces ⋮ Hawking's singularity theorem under a bounded integral norm of Ricci curvature

Cites Work

• Unnamed Item
• Comparison geometry for the Bakry-Emery Ricci tensor
• The upperbound of the volume expansion rate in a Lorentzian manifold
• Volume expansion rate of the Lorentzian manifold based on integral Ricci curvature over a timelike geodesic
• Volume comparison theorems for Lorentzian manifolds
• Relative volume comparison with integral curvature bounds
• Some geometric properties of the Bakry-Émery-Ricci tensor
• Some semi-Riemannian volume comparison theorems
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Distance to a focal point and singularity theorems with weak timelike convergence condition
• Optimal Transport

This page was built for publication: Volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci curvature bounds