Geodesic
Extension of locally holomorphic mappings into a product of complex manifolds
Izvestiya. Mathematics, Tome 27 (1986) no. 1, pp. 193-199 
S. M. Ivashkovich. Extension of locally holomorphic mappings into a product of complex manifolds. Izvestiya. Mathematics, Tome 27 (1986) no. 1, pp. 193-199. http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a10/
@article{IM2_1986_27_1_a10,
     author = {S. M. Ivashkovich},
     title = {Extension of locally holomorphic mappings into a~product of complex manifolds},
     journal = {Izvestiya. Mathematics},
     pages = {193--199},
     year = {1986},
     volume = {27},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that locally biholomorphic mappings from the punctured ball in $\mathbf C^n$ into a product of complex manifolds of positive dimension can be extended to the whole ball. In addition, it is proved that if complex manifolds $S_1$ and $S_2$ have the property that every locally biholomorphic map of the domain $D$ over $\mathbf C^n$ into $S_j$ can be holomorphically extended to the envelope of holomorphy $\widetilde D$ of $D$, then the product $S_1\times S_2$ possesses the same property. Bibliography: 6 titles