Isometric embedding of the 2-sphere with non negative curvature in \(\mathbb{R}^ 3\)

DOI10.1007/BF02572368zbMath0833.53049OpenAlexW2002815184MaRDI QIDQ1897990

Jia-Xing Hong, Claude Zuily

Publication date: 22 October 1995

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174776

zbMATH Keywords

Monge-Ampère equationnonnegative Gauss curvatureWeyl problem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (25)

Total mean curvature of the boundary and nonnegative scalar curvature fill-ins ⋮ The Dirichlet problem for degenerate curvature equations ⋮ Global Isometric Embedding of Surfaces in $$\mathbb R^3$$ ⋮ On a class of Hessian type equations on Riemannian manifolds ⋮ The Dirichlet problem for a class of prescribed curvature equations ⋮ Geometry, analysis, and morphogenesis: Problems and prospects ⋮ Regularity of a class of quasilinear degenerate elliptic equations ⋮ Isometric embedding in \(R^3\) of complete noncompact nonnegatively curved surfaces ⋮ Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds ⋮ Compactness of Alexandrov‐Nirenberg Surfaces ⋮ On a class of Hessian quotient type equations on Riemannian manifolds ⋮ Isometric embedding with nonnegative Gauss curvature under the graph setting ⋮ Alexandrov's isodiametric conjecture and the cut locus of a surface ⋮ Curvature estimates for immersed hypersurfaces in Riemannian manifolds ⋮ A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations ⋮ Quasi-spherical metrics and applications ⋮ A quasi-local mass for 2-spheres with negative Gauss curvature ⋮ Regularity of subelliptic Monge-Ampère equations in the plane ⋮ The semi-global isometric embedding of surfaces with curvature changing signs stably ⋮ Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ The Weyl problem of isometric immersions revisited ⋮ Weyl estimates for spacelike hypersurfaces in de Sitter space ⋮ The Gromov-Hausdorff hyperspace of nonnegatively curved $2$-spheres ⋮ A free boundary isometric embedding problem in the unit ball

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Neue a-priori-Abschätzungen für den Ortsvektor einer Fläche positiver Gaußscher Krümmung durch ihr Linienelement
• Dirichlet problems for general Monge-Ampère equations
• Isometric embeddings of surfaces with nonnegative curvature in \(\mathbb{R}^ 3\)
• \(C^\infty\) convex functions and manifolds of positive curvature
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Regularity of Solutions of Two-Dimensional Monge-Ampere Equations
• Monge-Ampere Equations on Convex Regions of The Plane
• On the regularity of the solution of then-dimensional Minkowski problem
• The Weyl and Minkowski problems in differential geometry in the large

This page was built for publication: Isometric embedding of the 2-sphere with non negative curvature in \(\mathbb{R}^ 3\)