A rigidity theorem of \(\alpha \)-relative parabolic hyperspheres

DOI10.1007/S00229-017-0918-7zbMath1380.53016OpenAlexW2588413910MaRDI QIDQ1679201

Ruiwei Xu, Ling-yun Zhu

Publication date: 8 November 2017

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-017-0918-7

zbMATH Keywords

\(\alpha\)-relative parabolic affine hypersphereBlaschke geometryLi-geometry

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Affine differential geometry (53A15)

Cites Work

• Hyperbolic relative hyperspheres with Li-normalization
• Hypersurfaces with Li-normalization and prescribed Gauss-Kronecker curvature
• A Liouville theorem for solutions of the Monge--Ampère equation with periodic data.
• Bernstein theorems for complete \(\alpha\)-relative extremal hypersurfaces
• Bernstein properties for some relative parabolic affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• A rigidity theorem for an affine Kähler-Ricci flat graph
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• An extension to a theorem of Jörgens, Calabi, and Pogorelov
• The Monge-Ampère equation
• Some aspects of the global geometry of entire space-like submanifolds
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