On the Hartogs-Bochner phenomenon for CR functions in \(P_2(\mathbb{C})\) (Q2782623)
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scientific article; zbMATH DE number 1725317
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Hartogs-Bochner phenomenon for CR functions in \(P_2(\mathbb{C})\) |
scientific article; zbMATH DE number 1725317 |
Statements
8 April 2002
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smooth hypersurfaces of the complex projective space
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holomorphic extension of CR functions
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jump formula
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global minimality
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one-sided neighborhood
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On the Hartogs-Bochner phenomenon for CR functions in \(P_2(\mathbb{C})\) (English)
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The authors give a simpler proof of a result of \textit{F. Sarkis} [Int. J. Math. 10, No. 7, 897-915 (1999; Zbl 1110.32308)]: Let \(M\) be a \(C^2\) real hypersurface in \(\mathbb{P}_n(\mathbb{C})\) \((n\geq 2)\) that divides the \(n\)-dimensional projective space into two connected open sets \(U^+\) and \(U^-\).NEWLINENEWLINENEWLINEIf \(M\) is globally minimal, i.e. if any two points of \(M\) can be joined by a piecewise smooth curve running in complex tangential directions, then all continuous CR meromorphic functions on \(M\) are boundary values of holomorphic functions defined on either one of the two sides \(U^+\), or \(U^-\).
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