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arXiv · 1610.06010

Regularity of complex geodesics and (non)-Gromov hyperbolicity of convex tube domains

Peter Pflug·Wlodzimierz Zwonek
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Abstract

We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains.The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry of non-Gromov hyperbolic convex domains. A connection between the Hilbert metric of a convex domain $\Omega$ in $\mathbb R^n$ with the Kobayashi distance of the tube domain over the domain $\Omega$ is also shown. Moreover, continuity properties up to the boundary of complex geodesics in tube domains with a smooth convex bounded base are also studied in detail.

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Peter Pflug, Wlodzimierz Zwonek. 2016-10-19. Regularity of complex geodesics and (non)-Gromov hyperbolicity of convex tube domains. https://arxiv.org/abs/1610.06010

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