Geodesic
Lemniscate Zone and Distortion Theorems for Multivalent Functions.~II
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 700-707

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For meromorphic circumferentially mean $p$-valent functions, an analog of the classical distortion theorem is proved. It is shown that the existence of connected lemniscates of the function and a constraint on a cover of two given points lead to an inequality involving the Green energy of a discrete signed measure concentrated at the zeros of the given function and the absolute values of its derivatives at these zeros. This inequality is an equality for the superposition of a certain univalent function and an appropriate Zolotarev fraction.
Keywords: meromorphic function, $p$-valent function, lemniscate, symmetrization.
Mots-clés : Zolotarev fraction 
@article{MZM_2018_104_5_a6,
     author = {V. N. Dubinin},
     title = {Lemniscate {Zone} and {Distortion} {Theorems} for {Multivalent} {Functions.~II}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {700--707},
     publisher = {mathdoc},
     volume = {104},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a6/}
}
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V. N. Dubinin. Lemniscate Zone and Distortion Theorems for Multivalent Functions.~II. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 700-707. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a6/