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Landau’s Theorem for Planar Harmonic Mappings

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Abstract

Landau gave a lower estimate for the radius of a schlicht disk centered at the origin and contained in the image of the unit disk under a bounded holomorphic function f normalized by f(0) = f′(0) − 1 = 1. Chen, Gauthier, and Hengartner established analogous versions for bounded harmonic functions. We improve upon their estimates.

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Authors and Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, Utah, 84602, USA

    Michael Dorff

  2. Department of Mathematics, Maria Curie-Sklodowska University, 20-031, Lublin, Poland

    Maria Nowak

Authors
  1. Michael Dorff
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  2. Maria Nowak
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Correspondence to Michael Dorff.

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Dorff, M., Nowak, M. Landau’s Theorem for Planar Harmonic Mappings. Comput. Methods Funct. Theory 4, 151–158 (2004). https://doi.org/10.1007/BF03321062

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  • DOI: https://doi.org/10.1007/BF03321062

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