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Diameter problems for univalent functions with quasiconformal extension

1992; Hindawi Publishing Corporation; Volume: 16; Issue: 4 Linguagem: Inglês

10.1155/s0161171293000857

1687-0425

Paul Deiermann,

Polymer Synthesis and Characterization

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.