Geodesic
Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem
Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 189-196.

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The author proves that functions holomorphic in a neighborhood of the set $D+i\partial E$, where $D$ and $E$ are domains in $\mathbf R^2$, extend holomorphically to a neighborhood of the set $D_1+iE$, where $D_1$ is a subdomain of $D$. As a corollary he shows that functions analytic along $D+i\gamma$, where $\gamma$ is a curve in $\mathbf R^2$, are single-valued in a neighborhood of $D+i\gamma$ under certain restrictions to the size of $D$ and $\gamma$. Bibliography: 4 titles. 
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     title = {Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem},
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S. M. Ivashkovich. Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem. Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 189-196. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a10/

[1] Andronikof E., “Valeurs au bord de fonctions holomorphes se recollant loin du réel”, C.R. Acad. Sc. Paris, 280 (1975), A-1427–1429 | MR | Zbl

[2] Napalkov V. V., “Ob odnom svoistve analiticheskogo prodolzheniya”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 367–372 | MR | Zbl

[3] Milnor Dzh., Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[4] Khermander L., Vvedenie v teoriyu analiticheskikh funktsii odnoi i neskolkikh kompleksnykh peremennykh, Mir, M., 1968