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arXiv · 1911.05632

Unbounded Kobayashi hyperbolic domains in $\mathbb C^n$

Hervé Gaussier·Nikolay Shcherbina
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Abstract

We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space $\mathbb C^n$ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in $\mathbb C^3$ that is Kobayashi hyperbolic and has a nonempty core. In particular, this domain is not biholomorphic to a bounded domain in $\mathbb C^3$ and the mentioned above sufficient condition for Kobayashi hyperbolicity is not necessary.

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Hervé Gaussier, Nikolay Shcherbina. 2020-05-07. Unbounded Kobayashi hyperbolic domains in $\mathbb C^n$. https://arxiv.org/abs/1911.05632

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