Hartogs-type extension for tube-like domains in C2

Albert Boggess, Roman J. Dwilewicz, Zbigniew Slodkowski

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we consider the Hartogs-type extension problem for unbounded domains in (Formula presented.). An easy necessary condition for a domain to be of Hartogs-type is that there is no a closed (in (Formula presented.)) complex variety of codimension one in the domain which is given by a holomorphic function smooth up to the boundary. The question is, how far this necessary condition is from the sufficient one? To show how complicated this question is, we give a class of tube-like domains which contain a complex line in the boundary which are either of Hartogs-type or not, depending on how the complex line is positioned with respect to the domain.

Original languageEnglish (US)
Pages (from-to)35-60
Number of pages26
JournalMathematische Annalen
Volume363
Issue number1-2
DOIs
StatePublished - Dec 23 2014

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Tube
Necessary Conditions
Line
Unbounded Domain
Codimension
Analytic function
Sufficient
Closed

Keywords

  • 32D15
  • Primary 32V10
  • Secondary 32V25

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hartogs-type extension for tube-like domains in C2. / Boggess, Albert; Dwilewicz, Roman J.; Slodkowski, Zbigniew.

In: Mathematische Annalen, Vol. 363, No. 1-2, 23.12.2014, p. 35-60.

Research output: Contribution to journalArticle

Boggess, Albert ; Dwilewicz, Roman J. ; Slodkowski, Zbigniew. / Hartogs-type extension for tube-like domains in C2. In: Mathematische Annalen. 2014 ; Vol. 363, No. 1-2. pp. 35-60.
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