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On a Hölder Constant in the Theory of Quasiconformal Mappings

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Abstract

A \(K\)-quasiconformal selfmap of the unit disk with identity boundary values satisfies the Hölder estimate

$$\begin{aligned} |f(z)-f(w)| \le 4^{1-1/K} |z-w|^{1/K}. \end{aligned}$$

The constant \(4^{1-1/K}\) is sharp.

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References

  1. Ahlfors, L.V.: Lectures on Quasiconformal Mappings. Van Nostrand Mathematical Studies, No. 10 (1966)

  2. Astala, K., Iwaniec, T., Martin, G.: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton Mathematical Series, vol. 48 (2009)

  3. Lehto, O., Virtanen, K.I.: Quasiconformal Mappings in the Plane, 2nd edn (1973). Translated from the German by K. W. Lucas, Die Grundlehren der mathematischen Wissenschaften, Band 126

  4. Mori, A.: On an absolute constant in the theory of quasi-conformal mappings. J. Math. Soc. Jpn. 8, 156–166 (1956)

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  5. Pommerenke, C.: Univalent Functions. Stud. Math. (1975). With a chapter on quadratic differentials by Gerd Jensen

  6. Vuorinen, M., Zhang, X.: Distortion of quasiconformal mappings with identity boundary values (2012, preprint). arXiv:1203.0427

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 , Helsinki, Finland

    István Prause

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  1. István Prause
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Correspondence to István Prause.

Additional information

Communicated by Matti Vuorinen.

Dedicated to the memory of F. W. Gehring.

The author was supported by the Academy of Finland Grant 1266182.

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Prause, I. On a Hölder Constant in the Theory of Quasiconformal Mappings. Comput. Methods Funct. Theory 14, 483–486 (2014). https://doi.org/10.1007/s40315-014-0060-4

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  • DOI: https://doi.org/10.1007/s40315-014-0060-4

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