Abstract:
An extremal problem of geometric function theory of a complex variable for the maximum
of products of the inner radii on a system of $n$ mutually non-overlapping multiply connected domains
$B_k$ containing the points $a_k$, $k=\overline{1,n}$, located on an arbitrary ellipse $\frac{x^2}{d^2}+\frac{y^2}{t^2}=1$ for which $d^2-t^2=1$,
is solved.
Keywords and phrases:inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Goluzin theorem.