Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds

DOI10.1515/crll.2003.003zbMath1091.53039arXivmath/0207054OpenAlexW2086952139MaRDI QIDQ4793827

Claus Gerhardt

Publication date: 16 February 2003

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0207054

zbMATH Keywords

prescribed scalar curvaturehypersurfacesstationary solutionLorentzian manifolds

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (15)

Evolution of spacelike surfaces in AdS\(_3\) by their Lagrangian angle ⋮ Existence and extendibility of rotationally symmetric graphs with a prescribed higher mean curvature function in Euclidean and Minkowski spaces ⋮ Curvature estimates of hypersurfaces in the Minkowski space ⋮ The global curvature estimate for the \(n - 2\) Hessian equation ⋮ Positive rotationally symmetric solutions for a Dirichlet problem involving the higher mean curvature operator in Minkowski space ⋮ Entire downward solitons to the scalar curvature flow in Minkowski space ⋮ Volume preserving curvature flows in Lorentzian manifolds ⋮ Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space ⋮ Curvature estimates for spacelike graphic hypersurfaces in Lorentz–Minkowski space R1n+1$\mathbb {R}^{n+1}_{1}$ ⋮ Locally constrained inverse mean curvature flow in GRW spacetimes ⋮ Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes. Application to the Minkowski problem in the Minkowski space ⋮ Orlicz-Minkowski flows ⋮ Parabolic approaches to curvature equations ⋮ Locally constrained inverse curvature flows ⋮ Global C²‐Estimates for Convex Solutions of Curvature Equations

Cites Work

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• Closed Weingarten hypersurfaces in Riemannian manifolds
• Erratum to: ``Hypersurfaces of prescribed Weingarten curvature
• The Large Scale Structure of Space-Time

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