Geodesic
Harmonic mappings and finite valency of analytic functions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 4, pp. 771-777

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The harmonic mappings of a circle into domains that can be cut into a finite number of convex subdomains has been studied. An estimate of the valency of holomorphic mappings of a circle composed of analytical components of the harmonic function has been obtained. In addition, the Keobe harmonic univalent function has been considered to illustrate the results of the research.
Keywords: harmonic function, univalent function, $n$-valent function, convex function, shear construction. 
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     author = {L. A. Xuan},
     title = {Harmonic mappings and finite valency of analytic functions},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {771--777},
     publisher = {mathdoc},
     volume = {160},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_4_a14/}
}
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L. A. Xuan. Harmonic mappings and finite valency of analytic functions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 4, pp. 771-777. http://geodesic.mathdoc.fr/item/UZKU_2018_160_4_a14/