Keywords
harmonic n-slit mappings, Clunie, Sheil-Small
Abstract
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). Faculty Publications. 651.
https://scholarsarchive.byu.edu/facpub/651
Document Type
Peer-Reviewed Article
Publication Date
1998-02-01
Permanent URL
http://hdl.lib.byu.edu/1877/1367
Publisher
First published in Proceedings of the American Mathematical Society Vol 128, no 2, published by the American Mathematical Society.
Language
English
College
Physical and Mathematical Sciences
Department
Mathematics
Copyright Status
© 1988 American Mathematical Society
Copyright Use Information
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