In this paper we consider the class of complex-valued harmonic univalent functions that map the unit disc onto the complex plane, half-plane or a strip slit along finitely many horizontal half-lines.
"Slit univalent harmonic mappings." Rocky Mountain J. Math. 46 (1) 169 - 187, 2016. https://doi.org/10.1216/RMJ-2016-46-1-169