Geodesic
Lemniscate zone and distortion theorems for multivalent functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 17-30

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The impact of the connectivity of some lemniscates of the multivalent function on the absolute value of this function or its derivative is considered. 
@article{ZNSL_2017_458_a2,
     author = {V. N. Dubinin},
     title = {Lemniscate zone and distortion theorems for multivalent functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--30},
     publisher = {mathdoc},
     volume = {458},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/}
}
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V. N. Dubinin. Lemniscate zone and distortion theorems for multivalent functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 17-30. http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/