Geometry of semi-tube domains in ℂ2

Josep M. Burgués; Roman J. Dwilewicz

doi:10.1515/advgeom-2012-0017

Geometry of semi-tube domains in ℂ²

Josep M. Burgués, Roman J. Dwilewicz

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	685-702
Journal	Advances in Geometry
Volume	12
Issue number	4
DOIs	https://doi.org/10.1515/advgeom-2012-0017
Publication status	Published - 1 Oct 2012

Keywords

Pseudoconvexity
Tubes
Unbounded domains

Access to Document

10.1515/advgeom-2012-0017

Cite this

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title = "Geometry of semi-tube domains in ℂ2",

abstract = "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. {\textcopyright} de Gruyter 2012.",

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T1 - Geometry of semi-tube domains in ℂ2

AU - Burgués, Josep M.

AU - Dwilewicz, Roman J.

PY - 2012/10/1

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N2 - 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.

AB - 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.

KW - Pseudoconvexity

KW - Tubes

KW - Unbounded domains

U2 - 10.1515/advgeom-2012-0017

DO - 10.1515/advgeom-2012-0017

M3 - Article

VL - 12

SP - 685

EP - 702

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-715X

IS - 4