The space of solutions to the Hessian one equation in the finitely punctured plane

DOI10.1016/J.MATPUR.2005.07.007zbMath1130.35052arXivmath/0411325OpenAlexW2004178563WikidataQ56885381 ScholiaQ56885381MaRDI QIDQ2581326

Yanyan Li

Publication date: 9 January 2006

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411325

zbMATH Keywords

Monge-Ampère equationparabolic affine spheresJörgens theorem

Mathematics Subject Classification ID

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

Related Items (16)

The Cauchy problem for improper affine spheres and the Hessian one equation ⋮ A Classification of Isolated Singularities of Elliptic Monge‐Ampére Equations in Dimension Two ⋮ Entire solutions of the degenerate Monge-Ampère equation with a finite number of singularities ⋮ Improper affine spheres and the Hessian one equation ⋮ The number of conformally equivalent maximal graphs ⋮ Affine hypersurfaces with parallel shape operator ⋮ Surfaces of constant curvature in \(\mathbb R^3\) with isolated singularities ⋮ Isolated singularities of graphs in warped products and Monge-Ampère equations ⋮ Solutions of some Monge-Ampère equations with isolated and line singularities ⋮ The Cauchy problem for indefinite improper affine spheres and their Hessian equation ⋮ Ribaucour type transformations for the Hessian one equation ⋮ An extension of the affine Bernstein problem ⋮ Singularities of improper affine maps and their Hessian equation ⋮ The affine Cauchy problem ⋮ Non-removable singularities of a fourth-order nonlinear partial differential equation ⋮ Existence of entire solutions of Monge-Ampère equations with prescribed asymptotic behavior

Cites Work

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• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• An extension to a theorem of Jörgens, Calabi, and Pogorelov
• Liouville property and regularity of a Hessian quotient equation

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