This article is cited in 1 paper

On the lemniscates of rational functions

V. N. Dubinin^a, A. S. Afanaseva-Grigoreva<sup>b

a</sup> Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: The impact of the connectivity of some lemniscates of the rational function on the absolute value of its derivative is considered. The role of the lemniscates in the problems of the extremal decomposition of the Riemann sphere is discussed.

Key words: rational function, lemniscate, extremal decomposition, condenser capacity, symmetrization.

UDC: 517.54

MSC: Primary 30C10; Secondary 30C15

Received: 12.06.2017

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