2009
DOI: 10.2422/2036-2145.2008.2.01
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A unified approach to the theory of separately holomorphic mappings

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 th… Show more

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Cited by 4 publications
(2 citation statements)
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“…Theorem 3.5) is a particular case of Theorem 10.4 (resp. Theorem 10.5) in [4]. However, the proofs of the latter theorems are analogous to those of the former ones.…”
mentioning
confidence: 80%
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“…Theorem 3.5) is a particular case of Theorem 10.4 (resp. Theorem 10.5) in [4]. However, the proofs of the latter theorems are analogous to those of the former ones.…”
mentioning
confidence: 80%
“…The purpose of this section is to derive from Theorem A in our previous work [4] and Theorem 1.1 a boundary cross theorem and a mixed cross theorem. We first recall some terminology and notation (relative to the system of conical approach regions) introduced in Section 2 of [4].…”
Section: Applicationsmentioning
confidence: 99%