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Minimal area problems for functions with integral representation

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Dov Aharonov

  2. Department of Mathematics, The Royal Institute of Technology, S-10044, Stockholm, Sweden

    Harold S. Shapiro

  3. Department of Mathematics and Statistics, Texas Tech University, Box 41042, 79409, Lubbock, TX, USA

    Alexander Yu. Solynin

Authors
  1. Dov Aharonov
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  2. Harold S. Shapiro
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  3. Alexander Yu. Solynin
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Corresponding author

Correspondence to Dov Aharonov.

Additional information

Supported by NSF grant DMS-0412908.

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Aharonov, D., Shapiro, H.S. & Solynin, A.Y. Minimal area problems for functions with integral representation. J. Anal. Math. 98, 83–111 (2006). https://doi.org/10.1007/BF02790271

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  • DOI: https://doi.org/10.1007/BF02790271

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