Geodesic
The problem of the regular isometric imbeddings and the Monge--Amp\`ere equation of the hyperbolic type
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 177-186

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A relationship between classical approaches to embeddings and the Monge–Ampère equations is described. A new method of constructing smooth solutions of the general Monge–Ampère equation of hyperbolic type for the domains of finite-stripe type is presented. Bibl. 18 titles. 
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     author = {E. V. Shikin},
     title = {The problem of the regular isometric imbeddings and the {Monge--Amp\`ere} equation of the hyperbolic type},
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     publisher = {mathdoc},
     volume = {234},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a12/}
}
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E. V. Shikin. The problem of the regular isometric imbeddings and the Monge--Amp\`ere equation of the hyperbolic type. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 177-186. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a12/