Geodesic
Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation
Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 319-326 Cet article a éte moissonné depuis la source Math-Net.Ru

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An (incomplete) Monge-Ampère equation is considered, as well as a domain where this equation has a regular solution. Estimates are established on the size of a rectangle that can be inscribed in this domain. The estimates depend on the equation, but not on its solution. Bibliography: 3 titles. 
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     author = {N. V. Efimov},
     title = {Estimates for the dimensions of the domains of regularity of solutions of certain {Monge{\textendash}Amp\`ere} equation},
     journal = {Sbornik. Mathematics},
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     year = {1976},
     volume = {29},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/}
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N. V. Efimov. Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 319-326. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/

[1] N. V. Efimov, “Issledovanie polnoi poverkhnosti otritsatelnoi krivizny”, DAN SSSR, 93:3 (1953), 393–395 | MR | Zbl

[2] N. V. Efimov, “Issledovanie odnoznachnoi proektsii poverkhnosti otritsatelnoi krivizny”, DAN SSSR, 93:4 (1953), 609–611 | MR | Zbl

[3] E. Heinz, “Über Flächen mit eineindeutiger Projektion auf eine Ebene, deren Krümmungen durch Ungleichungen eingeschränkt sind”, Math. Ann., 129:5 (1955), 451–454 | DOI | MR | Zbl