On the Boundary Behaviour of Univalent Harmonic Mappings onto Convex Domains



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].


Harmonic mapping analytic dilatation convex domains elliptic differential equation 

2000 MSC

26C10 30C15 


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Copyright information

© Heldermann  Verlag 2008

Authors and Affiliations

  • Daoud Bshouty
    • 1
  • Abdallah Lyzzaik
    • 2
  • Allen Weitsman
    • 3
  1. 1.Department of MathematicsTechnionHaifaIsrael
  2. 2.Department of MathematicsAmerican University of BeirutBeirutLebanon
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

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