A lower bound of the hyperbolic dimension for meromorphic functions having a logarithmic Hölder tract

Mayer, Volker

doi:10.1090/ecgd/320

A lower bound of the hyperbolic dimension for meromorphic functions having a logarithmic Hölder tract
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by Volker Mayer

Conform. Geom. Dyn. 22 (2018), 62-77

DOI: https://doi.org/10.1090/ecgd/320

Published electronically: June 27, 2018

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Abstract:

We improve existing lower bounds of the hyperbolic dimension for meromorphic functions that have a logarithmic tract $\Omega$ which is a Hölder domain. These bounds are given in terms of the fractal behavior, measured with integral means, of the boundary of $\Omega$ at infinity.

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