Geodesic
Complete Convex Solutions of Monge--Ampere-type Equations and Their Analogs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 147 (2018), pp. 51-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study complete convex solutions of certain nonlinear elliptic equations by using geometric methods. We present a proof of the Jörgens–Calabi–Pogorelov theorem about improper convex affine spheres based on the study of complete convex solutions of the simplest Monge–Ampere equation. We consider a similar problem for Monge–Ampere equations of more general type. We prove that, under certain assumptions, solutions of these equations are quadratic polynomials.
Keywords: improper convex affine sphere, Monge–Ampere equation. 
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V. N. Kokarev. Complete Convex Solutions of Monge--Ampere-type Equations and Their Analogs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 147 (2018), pp. 51-83. http://geodesic.mathdoc.fr/item/INTO_2018_147_a1/

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