The prescribed curvature problem for entire hypersurfaces in Minkowski space

DOI10.2140/apde.2024.17.1arXiv2007.04493WikidataQ128217023 ScholiaQ128217023MaRDI QIDQ6201394

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Publication date: 20 February 2024

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.04493

zbMATH Keywords

Minkowski spaceprescribed curvaturedownward translating solitons

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)

Cites Work

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• Hypersurfaces of prescribed curvature measure
• Embedded hyperspheres with prescribed mean curvature
• Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• The Dirichlet problem for Hessian equations on Riemannian manifolds
• On the Dirichlet problem for Hessian equations
• Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in \(\mathbb R^{n,1}\)
• The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
• Convex hypersurfaces of prescribed curvatures
• Spacelike hypersurfaces with constant Gauss-Kronecker curvature in the Minkowski space
• Translating solutions to mean curvature flow with a forcing term in Minkowski space
• Entire spacelike hypersurfaces with constant \(\sigma_k\) curvature in Minkowski space
• Entire spacelike hypersurfaces of prescribed scalar curvature in Minkowski space
• Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space
• The Christoffel-Minkowski problem. II: Weingarten curvature equations
• Dirichlet problem for the equation of a given Lorentz-Gaussian curvature
• Entire downward translating solitons to the mean curvature flow in Minkowski space
• Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space
• The Existence of Convex Body with Prescribed Curvature Measures
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• On the regularity of the solution of then-dimensional Minkowski problem
• On some inequalities for elementary symmetric functions
• A variational theory of the Hessian equation
• Hypersurfaces in IRⁿ⁺¹with prescribed gaussian curvature and related equations of monge—ampére type
• On the curvature estimates for Hessian equations
• Global C²‐Estimates for Convex Solutions of Curvature Equations
• Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
• The Weyl and Minkowski problems in differential geometry in the large
• An interior estimate for convex solutions and a rigidity theorem
• The global curvature estimate for the \(n - 2\) Hessian equation