Geodesic
The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy
Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 171-188 
N. V. Shcherbina. The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy. Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 171-188. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description is given of the set of those boundary points of a domain of holomorphy $D\subset\mathbf C^2$ which have a neighborhood in which the boundary fibers into analytic curves. For domains with $C^1$-smooth boundary whose closure has a basis of Stein neighborhoods this set coincides with the complement of the Shilov boundary $S_{A(\overline D)}$. 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] Rossi H., “The local maximum modulus principle”, Ann. Math., 72:1 (1960), 1–11 | DOI | MR | Zbl

[3] Bychkov S. N., “O geometricheskikh svoistvakh granitsy oblasti golomorfnosti”, Izv. AN SSSR. Ser. matem., 44:1 (1980), 46–62 | MR | Zbl

[4] Pflug P., “Über polynomiale Funktionen auf Holomorphiegebieten”, Math. Z., 139 (1974), 133–139 | DOI | MR | Zbl

[5] Hakim M., Sibony N., “Frontiere de Shilov et spectre de $A(D)$ pour des domains faiblement pseudoconvexes”, C.R. Acad. Sci., 285 (1975), 959–962 | MR