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On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
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Let Ω ⊂ Cn, n > 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of Cn \ Ω is Cn. It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in Cn for which the …