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 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.
@article{ASNSP_2008_5_7_2_181_0, 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}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 7}, number = {2}, year = {2008}, pages = {181-240}, zbl = {1241.32008}, mrnumber = {2437026}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2008_5_7_2_181_0} }
Nguyên, Viêt-Anh. A unified approach to the theory of separately holomorphic mappings. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 2, pp. 181-240. http://www.numdam.org/item/ASNSP_2008_5_7_2_181_0/
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