Diameter problems for univalent functions with quasiconformal extension

Paul Deiermann

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:378410

DOI: 10.1155/S0161171293000857

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