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Rippon, P. J. and Stallard, G. M.
(2018).
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.