Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature

DOI10.1007/s10455-023-09933-wMaRDI QIDQ6142742

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Publication date: 4 January 2024

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

zbMATH Keywords

Monge-Ampère equationgradient estimatesaffine Gauss curvaturecomplete centroaffine metrics

Mathematics Subject Classification ID

Applications of PDEs on manifolds (58J90) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Affine differential geometry (53A15)

Cites Work

• Hypersurfaces with Li-normalization and prescribed Gauss-Kronecker curvature
• Hypersurfaces with prescribed affine Gauss-Kronecker curvature
• Locally strongly convex hypersurfaces with constant affine mean curvature
• Centroaffine Bernstein problems
• On singular boundary value problems for the Monge-Ampère operator
• Boundary estimates of solutions for a class of Monge-Ampère equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Global affine differential geometry of hypersurfaces
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