Geodesic
On fibering into analytic curves of the common boundary of two domains of holomorphy
Izvestiya. Mathematics, Tome 21 (1983) no. 2, pp. 399-413 
N. V. Shcherbina. On fibering into analytic curves of the common boundary of two domains of holomorphy. Izvestiya. Mathematics, Tome 21 (1983) no. 2, pp. 399-413. http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a9/
@article{IM2_1983_21_2_a9,
     author = {N. V. Shcherbina},
     title = {On fibering into analytic curves of the common boundary of two domains of holomorphy},
     journal = {Izvestiya. Mathematics},
     pages = {399--413},
     year = {1983},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a9/}
}
TY  - JOUR
AU  - N. V. Shcherbina
TI  - On fibering into analytic curves of the common boundary of two domains of holomorphy
JO  - Izvestiya. Mathematics
PY  - 1983
SP  - 399
EP  - 413
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a9/
LA  - en
ID  - IM2_1983_21_2_a9
ER  - 
%0 Journal Article
%A N. V. Shcherbina
%T On fibering into analytic curves of the common boundary of two domains of holomorphy
%J Izvestiya. Mathematics
%D 1983
%P 399-413
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a9/
%G en
%F IM2_1983_21_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

An analogue of the Frobenius theorem is proved for the case of a continuous planar field. This leads to a proof that it is possible to fiber into analytic curves a $C^1$ smooth hypersurface in $\mathbf C^2$ on both sides of which lie domains of holomorphy. An example constructed of two domains of holomorphy with common boundary which does not contain analytic subsets. Bibliography: 5 titles.

[1] Sommer F., “Komplex-analytische Blättering reeler Mannigfaltigkeiten in $\mathbf C^m$”, Math. Ann., 136 (1958), 111–133 | DOI | MR | Zbl

[2] Kolmogorov A. H., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[3] Scherbina N. V., “Forma Levi dlya $C^1$-gladkikh giperpoverkhnostei i kompleksnaya struktura na granitse oblastei golomorfnosti”, Izv. AN SSSR. Ser. matem., 45:4 (1981), 874–895 | MR | Zbl

[4] Pflug P., “$C^\infty$-glattes streng pseudokonvexes Gebiet in $\mathbf C^3$ mit micht holomorph-konvexer Projection”, Abh. Math. Sem. Univ. Hamburg, 47 (1978), 92–94 | DOI | MR | Zbl

[5] Kasten V., “Über die Vererbung der Pseudokonvexität bei Projectionen”, Arch. Math., 34:4 (1980), 160–165 | DOI | MR | Zbl