Geodesic
Variations of Hartogs' Theorem
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 232-240

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Hartogs' separate analyticity theorem is extended to functions holomorphic along holomorphic curves that form mutually transversal foliations of the domain of definition of these functions. 
@article{TM_2006_253_a16,
     author = {E. M. Chirka},
     title = {Variations of {Hartogs'} {Theorem}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a16/}
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E. M. Chirka. Variations of Hartogs' Theorem. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 232-240. http://geodesic.mathdoc.fr/item/TM_2006_253_a16/