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.

DOI: https://doi.org/10.1007/s11854-018-0027-x

Abstract

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

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About

• Item ORO ID
• 41450
• Item Type
• Journal Item
• ISSN
• 1565-8538
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Bakers Conjecture and Eremenko's Conjecture: New Directions (XM-12-066-GS)	EP/K031163/1	EPSRC

• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2014 Springer
• Depositing User
• Philip Rippon