We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-2-5,
author = {Michael Dorff and Maria Nowak and Magdalena Wo\l oszkiewicz},
title = {Harmonic mappings onto parallel slit domains},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {149-162},
zbl = {1219.31001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-2-5}
}
Michael Dorff; Maria Nowak; Magdalena Wołoszkiewicz. Harmonic mappings onto parallel slit domains. Annales Polonici Mathematici, Tome 101 (2011) pp. 149-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-2-5/