Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes. Application to the Minkowski problem in the Minkowski space
From MaRDI portal
Publication:646397
DOI10.5802/aif.2622zbMath1234.53019arXiv0804.1053OpenAlexW1508791318MaRDI QIDQ646397
Thierry Barbot, François Béguin, Abdelghani Zeghib
Publication date: 17 November 2011
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0804.1053
Applications of global differential geometry to the sciences (53C80) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Foliations (differential geometric aspects) (53C12)
Related Items
Prescription of Gauss curvature using optimal mass transport, Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds, Spacelike convex surfaces with prescribed curvature in \((2+1)\)-Minkowski space, Regular domains and surfaces of constant Gaussian curvature in \(3\)-dimensional affine space, Fuchsian convex bodies: basics of Brunn-Minkowski theory, Prescription of Gauss curvature on compact hyperbolic orbifolds, Asymptotic behavior of Cauchy hypersurfaces in constant curvature space-times, A note on invariant constant curvature immersions in Minkowski space, On the volume of anti-de Sitter maximal globally hyperbolic three-manifolds, Affine deformations of quasi‐divisible convex cones, The equivariant Minkowski problem in Minkowski space, Constant Gauss curvature foliations of AdS spacetimes with particles, Clifford structures, bilegendrian surfaces, and extrinsic curvature, On the asymptotic geometry of finite-type \(k\)-surfaces in three-dimensional hyperbolic space, A cyclic extension of the earthquake flow. I, On the geometry of the initial singularity of globaly hyperbolic space-time, Constant scalar curvature hypersurfaces in \((3 + 1)\)-dimensional GHMC Minkowski spacetimes, Hyperbolic ends with particles and grafting on singular surfaces, Anti-de Sitter Geometry and Teichmüller Theory, The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry, Constant mean curvature foliation of globally hyperbolic \((2 + 1)\)-spacetimes with particles, Polynomial quadratic differentials on the complex plane and light-like polygons in the Einstein universe, Entire surfaces of constant curvature in Minkowski 3-space, Wild globally hyperbolic maximal anti‐de Sitter structures, Hypersurfaces of constant Gauss-Kronecker curvature with Li-normalization in affine space, The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Cosmological time versus CMC time in spacetimes of constant curvature
- Constant curvature foliations in asymptotically hyperbolic spaces
- Globally hyperbolic flat space--times
- Moduli of flat conformal structures of hyperbolic type
- Flat spacetimes with compact hyperbolic Cauchy surfaces
- Constant mean curvature foliations of simplicial flat spacetimes
- Minkowski type problems for convex hypersurfaces in the sphere
- Causal properties of AdS-isometry groups II. BTZ multi-black-holes
- Spacelike hypersurfaces with prescribed boundary values and mean curvature
- Foliations and laminations on hyperbolic surfaces
- Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
- Lines in space-times
- Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
- Flat conformal structures and the classification of de Sitter manifolds
- Monge-Ampère problems, holomorphic curves and laminations
- On the global evolution problem in \(2+1\) gravity
- Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in \(\mathbb R^{n,1}\)
- The Dirichlet problem for Weingarten hypersurfaces in Lorentz manifolds
- The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
- Constant mean curvature foliations of flat space-times
- On isometric immersions of the hyperbolic plane into the Lorentz- Minkowski space and the Monge-Ampère equation of a certain type
- Convex hypersurfaces of prescribed curvatures
- Foliations of globally hyperbolic spacetimes by CMC hypersurfaces
- Spacelike hypersurfaces with constant Gauss-Kronecker curvature in the Minkowski space
- Convex surfaces in Lorentzian spaces of constant curvature
- Constant mean curvature foliations of globally hyperbolic spacetimes locally modelled on \(Ad\, S_{3}\)
- Minimal surfaces and particles in 3-manifolds
- Lorentz spacetimes of constant curvature
- Entire spacelike hypersurfaces of prescribed scalar curvature in Minkowski space
- Riemannian structures of prescribed Gaussian curvature for compact 2- manifolds
- Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes
- Dirichlet problem for the equation of a given Lorentz-Gaussian curvature
- Hypersurfaces of prescribed curvature in Lorentzian manifolds
- Reduction of the Einstein equations in 2+1 dimensions to a Hamiltonian system over Teichmüller space
- Canonical Wick rotations in 3-dimensional gravity
- Problème de Minkowski et surfaces à courbure constante dans les variétés hyperboliques
- On the regularity of the solution of then-dimensional Minkowski problem
- The Dirichlet problem for Monge-Ampère equations in non-convex domains and spacelike hypersurfaces of constant Gauss curvature
- The cosmological time function
- Geodesic laminations with transverse hölder distributions1
- A generalized Minkowski problem with Dirichlet boundary condition
- Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds
- Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
- Domain of Dependence
- The Weyl and Minkowski problems in differential geometry in the large
- A Geometrical Background for De Sitter's World
- Geometry and spectra of compact Riemann surfaces
- Global affine differential geometry of hypersurfaces
- The topology and geometry of embedded surfaces of constant mean curvature
- Cosmological time in (2+1)-gravity