Geodesic
On $\Sigma$ – realizations of metrics of positive curvature
Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 515-525 Cet article a éte moissonné depuis la source Math-Net.Ru

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A metric $ds^2$ admits a $\Sigma$-realization if there is a realization of it in $E^3$ in the form of a surface whose boundary lies on a given surface $\Sigma$. This paper proves the existence of $\Sigma$-realizations of a certain class of metrics of positive curvature for surfaces of quite general form, and describes a number of possible $\Sigma$-realizations of the given metric. The proof is based on a consideration of a nonlinear boundary-value problem for immersion equations. Bibliography: 3 titles. 
@article{SM_1983_45_4_a7,
     author = {V. T. Fomenko},
     title = {On~$\Sigma$~{\textendash} realizations of metrics of positive curvature},
     journal = {Sbornik. Mathematics},
     pages = {515--525},
     year = {1983},
     volume = {45},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_4_a7/}
}
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%A V. T. Fomenko
%T On $\Sigma$ – realizations of metrics of positive curvature
%J Sbornik. Mathematics
%D 1983
%P 515-525
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%N 4
%U http://geodesic.mathdoc.fr/item/SM_1983_45_4_a7/
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V. T. Fomenko. On $\Sigma$ – realizations of metrics of positive curvature. Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 515-525. http://geodesic.mathdoc.fr/item/SM_1983_45_4_a7/

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[2] Sabitov I. X., “Ob odnoi skheme posledovatelnykh priblizhenii dlya pogruzhenii dvumernykh metrik v $E^3$”, Sib. matem. zh., XIX:6 (1978), 1358–1380 | MR

[3] Fomenko V. T., “Nepreryvnye izgibaniya vypuklykh poverkhnostei s kraevymi usloviyami”, Matem. sb., 110 (152) (1979), 493–504 | MR | Zbl