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.References
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Bibliographic Information
- Volker Mayer
- Affiliation: UFR de Mathématiques, UMR 8524 du CNRS, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 333982
- Email: volker.mayer@univ-lille.fr
- 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).
- © Copyright 2018 American Mathematical Society
- Journal: Conform. Geom. Dyn. 22 (2018), 62-77
- MSC (2010): Primary 30D05, 37F10
- DOI: https://doi.org/10.1090/ecgd/320
- MathSciNet review: 3817965