Geometry of Semi-tube Domains in ℂ2
Grundhöfer, Theo and Strambach, Karl
In this paper we study a class of unbounded domains in ℂ2 which are invariant with respect to translations in some fixed real direction. Such domains will be called semi-tubes. We prove various properties of such domains, e.g., dependence of pseudoconvexity on the position of the base of the domain in ℝ3 ≃ ℂ × ℝ the Hartogs type phenomenon on holomorphic extension of CR functions, and give concrete examples of semi-tubes over tori in ℝ3≃ℂ × ℝ and see how the position of the tori influences the pseudoconvexity of the semi-tube.
J. M. Burgués and R. Dwilewicz, "Geometry of Semi-tube Domains in ℂ2," Advances in Geometry, Walter de Gruyter, Jan 2012.
The definitive version is available at https://doi.org/10.1515/advgeom-2012-0017
Mathematics and Statistics
Keywords and Phrases
Tubes; unbounded domains; pseudoconvexity
Article - Journal
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