Geodesic
Envelopes of Holomorphy of Jordan Curves in~$\mathbb C^n$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 214-231

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A comprehensive answer is given to two related questions: (i) Can continuous functions be approximated by holomorphic ones on Jordan curves in $\mathbb C^n$ (A. G. Vitushkin, 1964)? (ii) Is any Jordan curve in $\mathbb C^n$ holomorphically convex (E.L. Stout, 1970)? 
@article{TM_2006_253_a15,
     author = {G. M. Henkin},
     title = {Envelopes of {Holomorphy} of {Jordan} {Curves} in~$\mathbb C^n$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {214--231},
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     year = {2006},
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     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a15/}
}
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G. M. Henkin. Envelopes of Holomorphy of Jordan Curves in~$\mathbb C^n$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 214-231. http://geodesic.mathdoc.fr/item/TM_2006_253_a15/