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.

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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. 
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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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[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