A Bernstein property of solutions to a class of prescribed affine mean curvature equations

DOI10.1007/S10455-006-9051-7zbMath1136.53007OpenAlexW2003143733MaRDI QIDQ2385166

James A. McCoy

Publication date: 11 October 2007

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

Full work available at URL: https://doi.org/10.1007/s10455-006-9051-7

zbMATH Keywords

Monge-Ampère type equationBernstein propertyglobal graphaffne maximal hypersurface

Mathematics Subject Classification ID

Boundary value problems for nonlinear higher-order PDEs (35G30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Affine differential geometry (53A15)

Related Items (6)

A Bernstein property of some fourth order partial differential equations ⋮ On Cauchy-Liouville-type theorems ⋮ Bernstein problem of affine maximal type hypersurfaces on dimension \(N \geq 3\) ⋮ A Bernstein theorem for affine maximal-type hypersurfaces ⋮ The Bernstein theorem for a class of fourth order equations ⋮ The Bernstein problem for affine maximal type hypersurfaces under decaying convexity

Cites Work

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• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• The Bernstein problem for affine maximal hypersurfaces
• Locally strongly convex hypersurfaces with constant affine mean curvature
• A Bernstein property of affine maximal hypersurfaces
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Properties of the solutions of the linearized Monge-Ampere equation

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