Volume preserving curvature flows in Lorentzian manifolds

DOI10.1007/s00526-011-0481-0zbMath1273.53060arXiv1104.2213OpenAlexW2117934701MaRDI QIDQ1937821

Matthias Makowski

Publication date: 1 February 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.2213

zbMATH Keywords

stabilitymean curvatureexponential convergenceglobally hyperboliccurvature estimateslong time existencevolume preservationshort time existenceglobally hyperbolic Lorentzian manifold\(n\)th root of the Gaussian curvaturefoliations of constant \(F\)-curvature hypersurfaces

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

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Cites Work

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• Volume-preserving flow by powers of the \(m\)th mean curvature
• The mixed volume preserving mean curvature flow
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Mixed volume preserving curvature flows
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes
• The scalar curvature flow in Lorentzian manifolds
• Curvature flows in semi-Riemannian manifolds
• The volume preserving mean curvature flow.
• Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds
• The Nemitskii Operator in Hölder Spaces: Some Necessary and Sufficient Conditions
• Volume preserving mean curvature flow in the hyperbolic space
• The Large Scale Structure of Space-Time
• Analysis II