Hartogs-type extension for tube-like domains in \(\mathbb C^2\)

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• 作者：Al Boggess ; Roman J. Dwilewicz ; Zbigniew Slodkowski
• 关键词：Primary 32V10 ; Secondary 32V25 ; 32D15
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：363
• 期：1-2
• 页码：35-60
• 全文大小：885 KB
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• 作者单位：Al Boggess (1)
  Roman J. Dwilewicz (2) (3)
  Zbigniew Slodkowski (4)
  
  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
  2. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409, USA
  3. Faculty of Mathematics, Cardinal Stefan Wyszy艅ski University, W贸ycickiego 1/3, 01-938, Warsaw, Poland
  4. Department of Mathematics, University of Illinois at Chicago, Chicago, IL, 60607, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

In this paper we consider the Hartogs-type extension problem for unbounded domains in \(\mathbb C^2\). An easy necessary condition for a domain to be of Hartogs-type is that there is no a closed (in \(\mathbb C^2\)) 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. Mathematics Subject Classification Primary 32V10 Secondary 32V25 32D15