Several complex variables are better than just one

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Abstract

In this popular expository article, we discuss some important ways in which complex analysis in more than one variable is different from complex analysis in one variable. Analytic continuation in several variables is contrasted with that in one variable, and the notion of psuedoconvexity is defined. Hartogs phenomenon and the Levi problem are also discussed in an informal way.

Original languageEnglish
Pages (from-to)754-769
Number of pages16
JournalResonance
Volume16
Issue number8
DOIs
StatePublished - Aug 2011

Keywords

  • Complex analysis
  • Hartogs phenomenon
  • Levi problem
  • domain of holomorphy
  • pseudoconvexity
  • several complex variables

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