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Diameter problems for univalent functions with quasiconformal extension

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  • Paul Deiermann

Abstract

This paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a complementary component of the image domain of a univalent function are extended. Applications to the transfinite diameters of families of non-overlapping functions and an extension of the Koebe one-quarter theorem are included.

Suggested Citation

  • Paul Deiermann, 1993. "Diameter problems for univalent functions with quasiconformal extension," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:378410
    DOI: 10.1155/S0161171293000857
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