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

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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. 
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     author = {N. V. Shcherbina},
     title = {On fibering into analytic curves of the common boundary of two domains of holomorphy},
     journal = {Izvestiya. Mathematics },
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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/