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Boundaries of univalent Baker domains

Rippon, P. J. and Stallard, G. M. (2018). Boundaries of univalent Baker domains. Journal d'Analyse Mathematique, 134(2) pp. 801–810.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s11854-018-0027-x
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Abstract

Let $f$ be a transcendental entire function and let $U$ be a univalent Baker domain of $f$. We prove a new result about the boundary behaviour of conformal maps and use this to show that the non-escaping boundary points of $U$ form a set of harmonic measure zero with respect to $U$. This leads to a new sufficient condition for the escaping set of $f$ to be connected, and also a new general result on Eremenko's conjecture.

Item Type: Journal Item
Copyright Holders: 2014 Springer
ISSN: 1565-8538
Project Funding Details:
Funded Project NameProject IDFunding Body
Bakers Conjecture and Eremenko's Conjecture: New Directions (XM-12-066-GS)EP/K031163/1EPSRC
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 41450
Depositing User: Philip Rippon
Date Deposited: 02 Dec 2014 10:23
Last Modified: 23 May 2019 14:28
URI: http://oro.open.ac.uk/id/eprint/41450
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