Diameter problems for univalent functions with quasiconformal extension

• Main Author: Paul Deiermann
• Format: Article
• Language: English
• Published: Hindawi Limited 1993-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: extremal problems; univalent functions; quasiconformal extensions; diameter theorems.
• Online Access: http://dx.doi.org/10.1155/S0161171293000857

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.