Geodesic
Smoothing and inversion of differential operators
Sbornik. Mathematics, Tome 17 (1972) no. 3, pp. 381-435

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Nash's implicit function theorem is generalized. The analytical results are applied to the problem of isometric immersion; in particular, the realizability in Euclidean space of real-analytic Riemannian manifolds is demonstrated. Moreover, theorems about the existence, approximation, extension and transversality of isometric immersion and related maps are stated; deformations and questions about unique definability are also investigated. In addition to the implicit function theorem, the theory of topological sheaves is used. Bibliography: 20 titles. 
@article{SM_1972_17_3_a4,
     author = {M. L. Gromov},
     title = {Smoothing and inversion of differential operators},
     journal = {Sbornik. Mathematics},
     pages = {381--435},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_3_a4/}
}
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M. L. Gromov. Smoothing and inversion of differential operators. Sbornik. Mathematics, Tome 17 (1972) no. 3, pp. 381-435. http://geodesic.mathdoc.fr/item/SM_1972_17_3_a4/