Geodesic
A unified approach to the theory of separately holomorphic mappings
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 2, pp. 181-240

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We extend the theory of separately holomorphic mappings between complex analytic spaces. Our method is based on Poletsky theory of discs, Rosay theorem on holomorphic discs and our recent joint-work with Pflug on boundary cross theorems in dimension 1. It also relies on our new technique of conformal mappings and a generalization of Siciak’s relative extremal function. Our approach illustrates the unified character: “From local information to global extensions”. Moreover, it avoids systematically the use of the classical method of doubly orthogonal bases of Bergman type.

Classification : 32D15, 32D10 
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     author = {Nguy\^en, Vi\^et-Anh},
     title = {A unified approach to the theory of separately holomorphic mappings},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {181--240},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {2},
     year = {2008},
     mrnumber = {2437026},
     zbl = {1241.32008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_181_0/}
}
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Nguyên, Viêt-Anh. A unified approach to the theory of separately holomorphic mappings. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 2, pp. 181-240. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_2_181_0/