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.
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Both authors are supported by EPSRC grant EP/K031163/1.
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Rippon, P.J., Stallard, G.M. Boundaries of univalent Baker domains. JAMA 134, 801–810 (2018). https://doi.org/10.1007/s11854-018-0027-x
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DOI: https://doi.org/10.1007/s11854-018-0027-x