The Cauchy problem for improper affine spheres and the Hessian one equation
From MaRDI portal
Publication:3443127
DOI10.1090/S0002-9947-07-04378-4zbMath1121.53008OpenAlexW2032047704MaRDI QIDQ3443127
José A. Gálvez, Juan A. Aledo, Rosa Maria Barreiro Chaves
Publication date: 31 May 2007
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04378-4
Nonlinear elliptic equations (35J60) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Affine differential geometry (53A15)
Related Items
A D'Alembert formula for flat surfaces in the 3-sphere, 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 Björling problem for timelike minimal surfaces in \({\mathbb {R}}^{4}_{1}\), Singularities of convex improper affine maps, The Björling problem for timelike surfaces in \(\mathbb R_2^4\), Surfaces of constant curvature in \(\mathbb R^3\) with isolated singularities, The Björling problem for prescribed mean curvature surfaces in \(\mathbb{R}^3\), Isolated singularities of graphs in warped products and Monge-Ampère equations, Björling problem for timelike surfaces in the Lorentz-Minkowski space, The Cauchy problem for indefinite improper affine spheres and their Hessian equation, Flat fronts in hyperbolic 3-space with prescribed singularities, Ribaucour type transformations for the Hessian one equation, The geometric Cauchy problem for the hyperbolic Hessian one equation, The indefinite affine Cauchy problem, An extension of the affine Bernstein problem, Complete Laguerre minimal surfaces in \(\mathbb R^3\), Singularities of improper affine maps and their Hessian equation, Singular improper affine spheres from a given Lagrangian submanifold, On the generalized Weyl problem for flat metrics in the hyperbolic 3-space, Improper affine maps, Ribaucour transformations for flat surfaces in the hyperbolic 3-space, The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group, The affine Cauchy problem, Even dimensional improper affine spheres, A characterization of hyperbolic affine flat, affine minimal surfaces in \(\mathbb{A}^3\), Non-removable singularities of a fourth-order nonlinear partial differential equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An extension of a theorem by K. Jörgens and a maximum principle at infinity for parabolic affine spheres
- Minimal Lagrangian diffeomorphisms and the Monge-Ampère equation
- Improper affine maps
- Symmetry and uniqueness of parabolic affine spheres
- Flat surfaces in the hyperbolic 3-space
- The Cauchy problem for the Liouville equation and Bryant surfaces
- Complete minimal Möbius strips in \(\mathbb R^n\) and the Björling problem
- Embedded isolated singularities of flat surfaces in hyperbolic 3-space
- Dense solutions to the Cauchy problem for minimal surfaces
- The space of solutions to the Hessian one equation in the finitely punctured plane
- Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
- Harmonische Abbildungen und die Differentialgleichung \(rt-s^2=1\)
- Complete affine hypersurfaces. Part I. The completeness of affine metrics
- Hypersurfaces with Maximal Affinely Invariant Area
- Björling problem for maximal surfaces in Lorentz–Minkowski space
- Global affine differential geometry of hypersurfaces
