Unbounded Kobayashi hyperbolic domains in \mathbb Cⁿ

2019/11/13 by Gaussier, Hervé, Shcherbina, Nikolay
#32Q45 #32U05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.05632

Abstract

We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space \mathbb Cⁿ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in \mathbb C³ that is Kobayashi hyperbolic and has a nonempty core. In particular, this domain is not biholomorphic to a bounded domain in \mathbb C³ and the mentioned above sufficient condition for Kobayashi hyperbolicity is not necessary.

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