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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Aharonov, D., Shapiro, H.S. & Solynin, A.Y. A minimal area problem in conformal mapping. J. Anal. Math. 78, 157–176 (1999). https://doi.org/10.1007/BF02791132
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DOI: https://doi.org/10.1007/BF02791132