Symmetry and uniqueness of parabolic affine spheres

DOI10.1007/BF01444223zbMath0873.53005OpenAlexW2047498997MaRDI QIDQ1923232

Yanyan Li

Publication date: 19 October 1997

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182989

zbMATH Keywords

Monge-Ampère equationlocally convex parabolic affine spheres

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Affine differential geometry (53A15)

Related Items (15)

The Cauchy problem for improper affine spheres and the Hessian one equation ⋮ Improper affine spheres and the Hessian one equation ⋮ Singly-periodic improper affine spheres. ⋮ Affine hemispheres of elliptic type ⋮ The Cauchy problem for indefinite improper affine spheres and their Hessian equation ⋮ Ribaucour type transformations for the Hessian one equation ⋮ The Geometry of Convex Affine Maximal Graphs ⋮ An extension of the affine Bernstein problem ⋮ Singularities of improper affine maps and their Hessian equation ⋮ Improper affine maps ⋮ Affine complete locally convex hypersurfaces ⋮ A Bernstein problem for special Lagrangian equations in exterior domains ⋮ A characterization of hyperbolic affine flat, affine minimal surfaces in \(\mathbb{A}^3\) ⋮ Non-removable singularities of a fourth-order nonlinear partial differential equation ⋮ The space of solutions to the Hessian one equation in the finitely punctured plane

Cites Work

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• A maximum principle at infinity for minimal surfaces and applications
• Symmetry and related properties via the maximum principle
• The spherical images of convex hypersurfaces
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• Elliptic Partial Differential Equations of Second Order
• Global affine differential geometry of hypersurfaces

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