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An Extension of Jenkin’s Condition for Extremal Domains Associated with the Univalent Bloch-Landau Constant

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Abstract

The univalent Bloch-Landau constant \(\cal U\) is the largest number such the image of the unit disk under any conformal map f must contain some disk of radius \({\cal U} \mid f^\prime (0)\mid\). We extend a condition, due to Jenkins, that extremal domains must meet. This condition is stated in terms of harmonic measure.

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Cork, Ireland

    Tom Carroll

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  1. Tom Carroll
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Correspondence to Tom Carroll.

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Dedicated to Walter Hayman, teacher and friend, on the occasion of his 80th birthday

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Carroll, T. An Extension of Jenkin’s Condition for Extremal Domains Associated with the Univalent Bloch-Landau Constant. Comput. Methods Funct. Theory 8, 159–165 (2008). https://doi.org/10.1007/BF03321679

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  • DOI: https://doi.org/10.1007/BF03321679

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