Bernstein theorems for complete \(\alpha\)-relative extremal hypersurfaces

DOI10.1007/s10455-012-9338-9zbMath1264.53014OpenAlexW2085685507MaRDI QIDQ1941758

Li Sheng, Ruiwei Xu, Min Xiong

Publication date: 21 March 2013

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

Full work available at URL: https://doi.org/10.1007/s10455-012-9338-9

zbMATH Keywords

Bernstein theoremblow-up analysisrelative extremal hypersurface

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Affine differential geometry (53A15)

Related Items (2)

A rigidity theorem of \(\alpha \)-relative parabolic hyperspheres ⋮ Bernstein properties for \(\alpha\)-complete hypersurfaces

Cites Work

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• A Bernstein theorem for the Abreu equation
• Hyperbolic relative hyperspheres with Li-normalization
• Hypersurfaces with Li-normalization and prescribed Gauss-Kronecker curvature
• Interior estimates for solutions of a fourth order nonlinear partial differential equation
• Bernstein properties for some relative parabolic affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• A Bernstein property of some fourth order partial differential equations
• Bending of simply supported incompressible saturated poroelastic beams with axial diffusion
• Affine complete locally convex hypersurfaces
• The Calabi conjecture on affine maximal surfaces

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