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 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.