Geometry of semi-tube domains in ℂ²

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. © de Gruyter 2012.