A unified approach to the theory of separately holomorphic mappings

Viêt-Anh Nguyên

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 2, page 181-240
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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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 7.2 (2008): 181-240. <http://eudml.org/doc/272276>.

@article{Nguyên2008,
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.},
author = {Nguyên, Viêt-Anh},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {separately holomorphic mapping; analytic spaces},
language = {eng},
number = {2},
pages = {181-240},
publisher = {Scuola Normale Superiore, Pisa},
title = {A unified approach to the theory of separately holomorphic mappings},
url = {http://eudml.org/doc/272276},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Nguyên, Viêt-Anh
TI - A unified approach to the theory of separately holomorphic mappings
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 2
SP - 181
EP - 240
AB - 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.
LA - eng
KW - separately holomorphic mapping; analytic spaces
UR - http://eudml.org/doc/272276
ER -

References

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