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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2012 Volume 404, Pages 100–119 (Mi znsl5262)

This article is cited in 1 paper

Generalized capacities, compound curves and removable sets

Yu. V. Dymchenkoa, V. A. Shlykb

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
b Far Eastern Federal University, Vladivostok, Russia

Abstract: Relations between the generalized capacity of a condenser in sense of Aikawa–Ohtsuka and the module of a family of compound curves connecting the condenser plates through a given set are established. Conditions of the removability of compact for the generalized capacity of a condenser are obtained.
Properties of the extremal length of vector measures are used.

Key words and phrases: generalized capacities, spherical symmetrization, removable sets.

UDC: 517.54+517.554

Received: 23.05.2012


 English version:
Journal of Mathematical Sciences (New York), 2013, 193:1, 55–65

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