Vol. 37, No. 3, 1971

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Conformal mappings onto ω-swirly domains

Carl Hanson Fitzgerald

Vol. 37 (1971), No. 3, 657–669

This paper introduces the concept of ω-swirly domains as a generalization of the notion of starlike domains. After analyzing certain geometric properties of this concept, some analytical properties of conformal mappings of the unit disc onto w-swirly domains are developed. The main theorem determines the maximum radius rω for which {z : |z| < rω} is mapped onto an ω-swirly domain by all schlicht functions on the unit disc; thus it gives an estimate of the twistedness of the images of subdiscs centered at the origin under conformal mappings of the unit disc. Comparisons are then made between the concept of ω-swirly and other geometric notions in the theory of conformal mapping.

Mathematical Subject Classification
Primary: 30A32
Received: 25 June 1969
Revised: 6 August 1970
Published: 1 June 1971
Carl Hanson Fitzgerald