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Conformal Geometry and Dynamics

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


Author: Volker Mayer
Journal: Conform. Geom. Dyn. 22 (2018), 62-77
MSC (2010): Primary 30D05, 37F10
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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Additional Information

Volker Mayer
Affiliation: UFR de Mathématiques, UMR 8524 du CNRS, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France
Email: volker.mayer@univ-lille.fr

DOI: https://doi.org/10.1090/ecgd/320
Received by editor(s): September 13, 2017
Received by editor(s) in revised form: April 9, 2018
Published electronically: June 27, 2018
Additional Notes: This research was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01).
Article copyright: © Copyright 2018 American Mathematical Society

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