Hartogs-Bochner type theorem in projective space

Mathematics – Complex Variables

Scientific paper

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23 pages, version with minor corrections

Scientific paper

We prove the following Hartogs-Bochner type theorem: Let $M$ be a
connected $C^2$ hypersurface of $P_n(\mathbb{C})$ ($n\geq 2$) which divides
$P_n(\mathbb{C})$ in two connected open sets $\Omega_1$ and $\Omega_2$. Then
there exists $i \in \{1,2\}$ such that $C^{1}$ CR functions defined on $M$
extends holomorphically to $\Omega_i$.

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