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Generalized capacities, compound curves, and removable sets

Relations between the generalized capacity of a condenser in the sense of Aikawa-Ohtsuka and the module of the family of compound curves connecting the condenser plates through a given set are established. Conditions of the removability of a compact set for the generalized capacity of a condenser are obtained. Properties of the extremal length of vector measures are used. Bibliography: 9 titles.


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Correspondence to Yu. V. Dymchenko.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 100–119.

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Dymchenko, Y.V., Shlyk, V.A. Generalized capacities, compound curves, and removable sets. J Math Sci 193, 55–65 (2013).

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  • Vector Measure
  • Generalize Capacity
  • Extremal Length
  • Compound Curf