Abstract
The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, Δ, such that f = h+ḡ where h(z) = z + ∑2∞ akzk g(z) = ∑1∞ bkzk. SHO 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 SHO. 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. ©1998 American Mathematical Society.
Recommended Citation
M. Dorff, "Some Harmonic N-Slit Mappings," Proceedings of the American Mathematical Society, vol. 126, no. 2, pp. 569 - 576, American Mathematical Society, Jan 1998.
The definitive version is available at https://doi.org/10.1090/s0002-9939-98-04105-7
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
0002-9939
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 American Mathematical Society, All rights reserved.
Publication Date
01 Jan 1998
