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A minimal area problem in conformal mapping |
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| Authors: | Dov Aharonov Harold S. Shapiro Alexander Yu. Solynin |
| Affiliation: | (1) Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel;(2) Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden;(3) V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191011 St. Petersburg, Russia |
| Abstract: | LetS denote the usual class of functionsf holomorphic and univalent in the unit diskU such thatf(0)=f′(0)−1=0. The main result of the paper is that area (f(U) ≥27π/7)(2-α)−2 for allf∈S such that |f″(0)|=2α, 1/2<α<2. This solves a long-standing extremal problem for the class of functions considered. |
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