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arXiv · 1403.7673

Gromov (non)hyperbolicity of certain domains in $\mathbb{C}^{2}$

Nikolai Nikolov·Pascal J. Thomas·Maria Trybula
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Abstract

We prove the non-hyperbolicity of the Kobayashi distance for $\mathcal{C}^{1,1}$-smooth convex domains in $\mathbb{C}^{2}$ which contain an analytic disc in the boundary or have a point of infinite type with rotation symmetry. Moreover, examples of smooth, non pseudoconvex, Gromov hyperbolic domains are given; we prove that the symmetrized polydisc and the tetrablock are not Gromov hyperbolic and write down some results about Gromov hyperbolicity of product spaces.

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Nikolai Nikolov, Pascal J. Thomas, Maria Trybula. 2014-03-29. Gromov (non)hyperbolicity of certain domains in $\mathbb{C}^{2}$. https://doi.org/10.1515/forum-2014-0113

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