On the Hartogs–Bochner phenomenon for CR functions in 𝑃₂(ℂ)

Dwilewicz, Roman; Merker, Joël

doi:10.1090/S0002-9939-02-06357-8

On the Hartogs–Bochner phenomenon for CR functions in $P_2(\mathbb {C})$
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Proc. Amer. Math. Soc. 130 (2002), 1975-1980 Request permission

Abstract:

Let $M$ be a compact, connected, $\mathcal {C}^2$-smooth and globally minimal hypersurface $M$ in $P_2(\mathbb {C})$ which divides the projective space into two connected parts $U^{+}$ and $U^{-}$. We prove that there exists a side, $U^-$ or $U^+$, such that every continuous CR function on $M$ extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.

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