harmonic n-slit mappings, Clunie, Sheil-Small
The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h+g where h(z) = (see PDF), g(z) = (see PDF) . SOH will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SOH. Finally we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius.
Original Publication Citation
Proceedings of the American Mathematical Society, Vol 128, no 2, pp 569-576.
BYU ScholarsArchive Citation
Dorff, Michael, "Some harmonic n-slit mappings" (1998). All Faculty Publications. 651.
First published in Proceedings of the American Mathematical Society Vol 128, no 2, published by the American Mathematical Society.
Physical and Mathematical Sciences
© 1988 American Mathematical Society
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