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A uniqueness result in conformal mapping. II


Author: James A. Jenkins
Journal: Proc. Amer. Math. Soc. 85 (1982), 231-232
MSC: Primary 30C55
DOI: https://doi.org/10.1090/S0002-9939-1982-0652448-7
MathSciNet review: 652448
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Abstract: This paper gives an elementary proof of the result that for a function $ f$ in the family $ \Sigma $ the diameter of the complement of the image of $ \left\vert z \right\vert > 1$ by $ w = f(z)$ attains its minimal value 2 only for $ f(z) = z + c$, $ c$ constant.


References [Enhancements On Off] (What's this?)

  • [1] James A. Jenkins, Univalent functions and conformal mapping, Springer-Verlag, Berlin-- Göttingen-Heidelberg, 1958. MR 0096806 (20:3288)
  • [2] -, A uniqueness result in conformal mapping, Proc. Amer. Math. Soc. 22 (1969), 324-325. MR 0241619 (39:2958)
  • [3] A. Pfluger, On a uniqueness theorem in conformal mapping, Michigan Math. J. 23 (1976), 363-- 365. MR 0442207 (56:593)
  • [4] -, On the diameter of planar curves and Fourier coefficients, J. Appl. Math. Phys. 30 (1979), 305-314. MR 535988 (81b:42024)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0652448-7
Article copyright: © Copyright 1982 American Mathematical Society

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