For citation:
Zherdev A. V. An Asymptotic Relation for Conformal Radii of Two Nonoverlapping Domains. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 3, pp. 274-283. DOI: 10.18500/1816-9791-2018-18-3-274-283, EDN: YBMQIH
An Asymptotic Relation for Conformal Radii of Two Nonoverlapping Domains
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 obtainan a symptotic 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.
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