Some a priori bounds for solutions of the constant Gauss curvature equation.

DOI10.1016/S0022-0396(03)00171-2zbMath1160.53357OpenAlexW1970701852MaRDI QIDQ1413203

Rafael López

Publication date: 16 November 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-0396(03)00171-2

zbMATH Keywords

Gauss curvatureA priori estimatesSecond fundamental form

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) A priori estimates in context of PDEs (35B45) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• Locally convex hypersurfaces of prescribed curvature and boundary
• Boundary-value problems on \(S^ n\) for surfaces of constant Gauss curvature
• The Gauss map and second fundamental form of surfaces in \(\mathbb{R}^3\)
• The existence of hypersurfaces of constant Gauss curvature with prescribed boundary.
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The neumann problem for equations of monge-ampère type
• Boundary value problems for surfaces of constant Gauss Curvature
• Hypersurfaces of prescribed Gauss curvature and boundary in Riemannian manifolds
• On locally convex hypersurfaces with boundary

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