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On extremal quasiconformal extensions of conformal mappings

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Abstract

Letf(t, z)=z+tω(1/z) be schlicht for ⋎z⋎>1, ω(z) = Σ = 0/∞ n a n z n,t>0. The paper considers first-order estimates for the dilatation of extremal quasiconformal extensions off ast→0.

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References

  1. Lars V. Ahlfors,Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math.74 (1961), 171–191.

    Article  MathSciNet  Google Scholar 

  2. Reiner Kühnau,Verzerrungssätze und Koeffizientenbedingungen vom Grunskyschen Typ für quasikonforme Abbildungen, Math. Nachr.48 (1971), 77–105.

    Article  MATH  MathSciNet  Google Scholar 

  3. Olli Lehto,Schlicht functions with a quasiconformal extension, Ann. Acad. Sci. Fenn. Ser. AI500 (1971), 10 pp.

  4. Chr. Pommerenke,Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975, Chapter 9.

    MATH  Google Scholar 

  5. Edgar Reich and Kurt Strebel,Extremal quasiconformal mappings with given boundary values, in Contributions to Analysis, a Collection of Papers Dedicated to Lipman Bers, Academic Press, 1974.

  6. M. Schiffer and G. Schober,Coefficient problems and generalized Grunsky inequalities, Arch. Rational Mech. Anal.60 (1976), 205–228.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota, USA

    Edgar Reich

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  1. Edgar Reich
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Additional information

This work was initiated during the Special Year in Complex Analysis at the Technion, and was supported in parts by the Samuel Neaman Fund, the Forschungsinstitut für Mathematik, ETH, Zürich, and the National Science Foundation.

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Reich, E. On extremal quasiconformal extensions of conformal mappings. Israel J. Math. 28, 91–97 (1977). https://doi.org/10.1007/BF02759783

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  • DOI: https://doi.org/10.1007/BF02759783

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