A free boundary problem associated with the isoperimetric inequality

  • Artem Abanov
  • Catherine Bénéteau
  • Dmitry KhavinsonEmail author
  • Razvan Teodorescu


This paper proves a 30-year-old conjecture that disks and annuli are the only domains where analytic content—the uniform distance from \(\bar z\) to analytic functions—achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin’s problem about laminary flow of incompressible viscous fluid for multiply-connected domains, and Garabedian’s problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed.


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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Artem Abanov
    • 1
  • Catherine Bénéteau
    • 2
  • Dmitry Khavinson
    • 2
    Email author
  • Razvan Teodorescu
    • 2
  1. 1.Department of Physics & Astronomy, MS 4242Texas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

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