A unified approach to the theory of separately holomorphic mappings

Nguyên, Viêt-Anh

Nguyên, Viêt-Anh

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 2, p. 181-240

Abstract

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.

MR 2437026 | Zbl 1241.32008

Classification: 32D15, 32D10

@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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