The affine complete hypersurfaces of constant Gauss-Kronecker curvature

DOI10.1007/s10114-009-7063-5zbMath1173.53008OpenAlexW2118516854MaRDI QIDQ839767

Bao Fu Wang

Publication date: 3 September 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-009-7063-5

zbMATH Keywords

Monge-Ampère equationaffine Gauss-Kronecker curvaturenonlinear fourth order PDEcompleteness in affine hypersurface theory

Mathematics Subject Classification ID

Boundary value problems for nonlinear higher-order PDEs (35G30) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Boundary value problems on manifolds (58J32) Affine differential geometry (53A15)

Cites Work

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• Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Centroaffine Bernstein problems
• Spacelike hypersurfaces with constant Gauss-Kronecker curvature in the Minkowski space
• Euclidean complete hypersurfaces with negative constant affine mean curvature
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Global affine differential geometry of hypersurfaces