A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 4 (2005) no. 2, p. 219-254
Using recent development in Poletsky theory of discs, we prove the following result: Let X, Y be two complex manifolds, let Z be a complex analytic space which possesses the Hartogs extension property, let A (resp. B) be a non locally pluripolar subset of X (resp. Y). We show that every separately holomorphic mapping f:W:=(A×Y)(X×B)Z extends to a holomorphic mapping f ^ on W ^:=(z,w)X×Y:ω ˜(z,A,X)+ω ˜(w,B,Y)<1 such that f ^=f on WW ^, where ω ˜(·,A,X) (resp. ω ˜(·,B,Y)) is the plurisubharmonic measure of A (resp. B) relative to X (resp. Y). Generalizations of this result for an N-fold cross are also given.
Classification:  32D15,  32D10
@article{ASNSP_2005_5_4_2_219_0,
     author = {Nguy\^en, Vi\^et-Anh},
     title = {A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {2},
     year = {2005},
     pages = {219-254},
     zbl = {1170.32306},
     mrnumber = {2163556},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2005_5_4_2_219_0}
}
Nguyên, Viêt-Anh. A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 4 (2005) no. 2, pp. 219-254. http://www.numdam.org/item/ASNSP_2005_5_4_2_219_0/

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