Geodesic
An asymptotic relation for conformal radii of two nonoverlapping domains
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 3, pp. 274-283

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We consider a family of continuously varying closed Jordan curves given by a polar equation, such that the interiors of the curves form an increasing or decreasing chain of domains. Such chains can be described by the Löwner – Kufarev differential equation. We deduce an integral representation of a driving function in the equation. Using this representation we obtain an asymptotic formula, which establishes a connection between conformal radii of bounded and unbounded components of the complement of the Jordan curve when the bounded component is close to the unit disk. 
@article{ISU_2018_18_3_a2,
     author = {A. V. Zherdev},
     title = {An asymptotic relation for conformal radii of two nonoverlapping domains},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {274--283},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ISU_2018_18_3_a2/}
}
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A. V. Zherdev. An asymptotic relation for conformal radii of two nonoverlapping domains. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 3, pp. 274-283. http://geodesic.mathdoc.fr/item/ISU_2018_18_3_a2/