Geodesic
Lemniscates and Inequalities for the Logarithmic Capacities of Continua
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 33-37.

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It is shown that if $P(z)=z^n+\dotsb$ is a polynomial with connected lemniscate $E(P)=\{z\colon |P(z)|\le 1\}$ and $m$ critical points, then, for any $n-m+1$ points on the lemniscate $E(P)$, there exists a continuum $\gamma\subset E(P)$ of logarithmic capacity $\operatorname{cap}\gamma\le 2^{-1/n}$ which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.
Keywords: lemniscate of a polynomial, logarithmic capacity, continuum. 
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V. N. Dubinin. Lemniscates and Inequalities for the Logarithmic Capacities of Continua. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 33-37. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a4/

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