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On the Boundary Behaviour of Univalent Harmonic Mappings onto Convex Domains

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Abstract

In this note we discuss the boundary behavior of a univalent harmonic mapping f from the unit disk U “onto” a bounded convex domain Ω in the sense of Hengartner and Schober, whose second dilatation function a is an inner function. This problem was raised by Laugesen in [10].

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Authors and Affiliations

  1. Department of Mathematics, Technion, Haifa, 32000, Israel

    Daoud Bshouty

  2. Department of Mathematics, American University of Beirut, Beirut, Lebanon

    Abdallah Lyzzaik

  3. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-1395, USA

    Allen Weitsman

Authors
  1. Daoud Bshouty
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  2. Abdallah Lyzzaik
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  3. Allen Weitsman
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Corresponding author

Correspondence to Daoud Bshouty.

Additional information

Dedicated to Walter Hayman on his 80th birthday

The first author thanks the Promotion of Research Fund at the Technion for its support.

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Bshouty, D., Lyzzaik, A. & Weitsman, A. On the Boundary Behaviour of Univalent Harmonic Mappings onto Convex Domains. Comput. Methods Funct. Theory 8, 261–275 (2008). https://doi.org/10.1007/BF03321687

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  • DOI: https://doi.org/10.1007/BF03321687

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