A uniqueness result in conformal mapping. II
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- by James A. Jenkins PDF
- Proc. Amer. Math. Soc. 85 (1982), 231-232 Request permission
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 $\left | z \right | > 1$ by $w = f(z)$ attains its minimal value 2 only for $f(z) = z + c$, $c$ constant.References
- James A. Jenkins, Univalent functions and conformal mapping, Reihe: Moderne Funktionentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0096806
- James A. Jenkins, A uniqueness result in conformal mapping, Proc. Amer. Math. Soc. 22 (1969), 324–325. MR 241619, DOI 10.1090/S0002-9939-1969-0241619-3
- Albert Pfluger, On a uniqueness theorem in conformal mapping, Michigan Math. J. 23 (1976), no. 4, 363–365 (1977). MR 442207
- Albert Pfluger, On the diameter of planar curves and Fourier coefficients, Z. Angew. Math. Phys. 30 (1979), no. 2, 305–314 (English, with German summary). MR 535988, DOI 10.1007/BF01601942
Additional Information
- © Copyright 1982 American Mathematical Society
- 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