Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space

DOI10.1515/CRELLE.2006.047zbMath1097.53040arXivmath/0611909OpenAlexW2963083130WikidataQ125025346 ScholiaQ125025346MaRDI QIDQ5479406

Huai-Yu Jian, Bo Guan, Richard M. Schoen

Publication date: 7 July 2006

Full work available at URL: https://arxiv.org/abs/math/0611909

zbMATH Keywords

prescribed Gauss curvature in Minkowski spacespace-like convex hypersurfaces of positive constant (K-hypersurfaces)

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Optimization of shapes other than minimal surfaces (49Q10) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (15)

Entire spacelike hypersurfaces with constant \(\sigma_k\) curvature in Minkowski space ⋮ Spacelike convex surfaces with prescribed curvature in \((2+1)\)-Minkowski space ⋮ Rigidity of isometric immersions into the light cone ⋮ The equivariant Minkowski problem in Minkowski space ⋮ Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space ⋮ Entire self-expanders for power of \(\sigma_k\) curvature flow in Minkowski space ⋮ Rotational \(K^{\alpha}\)-translators in Minkowski space ⋮ The prescribed curvature problem for entire hypersurfaces in Minkowski space ⋮ Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes. Application to the Minkowski problem in the Minkowski space ⋮ Exterior Dirichlet problem for translating solutions of Gauss curvature flow in Minkowski space ⋮ Entire surfaces of constant curvature in Minkowski 3-space ⋮ Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature ⋮ Spacelike hypersurfaces of prescribed Gauss-Kronecker curvature in exterior domains ⋮ Hypersurfaces of constant Gauss-Kronecker curvature with Li-normalization in affine space ⋮ Translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space

Cites Work

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• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
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• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• On isometric immersions of the hyperbolic plane into the Lorentz- Minkowski space and the Monge-Ampère equation of a certain type
• Spacelike hypersurfaces with constant Gauss-Kronecker curvature in the Minkowski space
• Dirichlet problem for the equation of a given Lorentz-Gaussian curvature
• Locally convex hypersurfaces of constant curvature with boundary
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The Dirichlet problem for Monge-Ampère equations in non-convex domains and spacelike hypersurfaces of constant Gauss curvature

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