On the Darboux-Picard theorem in \({\mathbf C}^ n\) (Q1330164)
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scientific article; zbMATH DE number 614391
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Darboux-Picard theorem in \({\mathbf C}^ n\) |
scientific article; zbMATH DE number 614391 |
Statements
On the Darboux-Picard theorem in \({\mathbf C}^ n\) (English)
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17 August 1994
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Theorem. Let \(D \subset \mathbb{C}^ n\), \(n \geq 2\), be a bounded domain with \(bD\) homeomorphic to \(S^{2n-1}\), and let \(f = (f_ 1, \dots, f_ n) : \overline D \to \mathbb{C}^ n\) be a mapping such that \(f_ j\) is holomorphic in \(D\) and continuous on \(\overline D\). Then if \(f\) is one- to-one on \(bD\), \(f\) is one-to-one throughout \(\overline D\).
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Darboux-Picard theorem
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holomorphic function
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one-to-one
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0.730530858039856
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0.7240481972694397
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