On necessary and sufficient conditions for the Kobayashi hyperbolicity of tube domains in C2

Alexander Isaev

    Research output: Contribution to journalArticlepeer-review

    Abstract

    This note concerns tube domains in C2 with the envelope of holomorphy not equal to the entire space. We construct examples showing that for such domains the sufficient condition for Kobayashi hyperbolicity due to M. Jarnicki and P. Pflug cannot be replaced by its weaker “affine” variant, which is known to be a necessary condition for hyperbolicity. Thus, we arrive at the somewhat unexpected conclusion that the obstructions for a domain in the above class to be Kobayashi hyperbolic are not just “affine”.

    Original languageEnglish
    Pages (from-to)58-62
    Number of pages5
    JournalJournal of Mathematical Analysis and Applications
    Volume460
    Issue number1
    DOIs
    Publication statusPublished - 1 Apr 2018

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