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. 
@article{INTO_2018_147_a1,
     author = {V. N. Kokarev},
     title = {Complete {Convex} {Solutions} of {Monge--Ampere-type} {Equations} and {Their} {Analogs}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {51--83},
     publisher = {mathdoc},
     volume = {147},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_147_a1/}
}
TY  - JOUR
AU  - V. N. Kokarev
TI  - Complete Convex Solutions of Monge--Ampere-type Equations and Their Analogs
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 51
EP  - 83
VL  - 147
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_147_a1/
LA  - ru
ID  - INTO_2018_147_a1
ER  - 
%0 Journal Article
%A V. N. Kokarev
%T Complete Convex Solutions of Monge--Ampere-type Equations and Their Analogs
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 51-83
%V 147
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_147_a1/
%G ru
%F INTO_2018_147_a1
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/