Hartogs-type extension for tube-like domains in C2

Albert Boggess, Roman J. Dwilewicz, Zbigniew Slodkowski

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we consider the Hartogs-type extension problem for unbounded domains in C2. An easy necessary condition for a domain to be of Hartogs-type is that there is no a closed (in C2) 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 - Oct 13 2015

Keywords

  • 32D15
  • Primary 32V10
  • Secondary 32V25

ASJC Scopus subject areas

  • Mathematics(all)

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