Minimal area problems for functions with integral representation

  • Dov Aharonov
  • Harold S. Shapiro
  • Alexander Yu. Solynin


We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal areaa 2-problem for convex functions and for typically real functions. The latter gives a new solution to the minimal areaa 2-problem for the classS of normalized univalent functions in the unit disc.


Univalent Function Conformal Mapping Bergman Space Minimal Area Extremal Function 
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Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  • Dov Aharonov
    • 1
  • Harold S. Shapiro
    • 2
  • Alexander Yu. Solynin
    • 3
  1. 1.Department of MathematicsThe Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of MathematicsThe Royal Institute of TechnologyStockholmSweden
  3. 3.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

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