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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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A lower bound of the hyperbolic dimension for meromorphic functions having a logarithmic Hölder tract
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by Volker Mayer PDF
Conform. Geom. Dyn. 22 (2018), 62-77 Request permission

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
  • 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