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

2017/11/13 by Alexander Isaev, Isaev, Alexander
Mathematics · #32A07 #32Q45 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1711.04487

openalex publication_date 2017/11/13 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

This note concerns tube domains in mathbb C² with the envelope of\nholomorphy not equal to the entire space. We construct examples showing that\nfor such domains the sufficient condition for Kobayashi hyperbolicity due to M.\nJarnicki and P. Pflug cannot be replaced by its weaker "affine" variant, which\nis known to be a necessary condition for hyperbolicity. Thus, we arrive at the\nsomewhat unexpected conclusion that the obstructions for a domain in the above\nclass to be Kobayashi hyperbolic are not just "affine".\n

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