Generalized capacities, compound curves, and removable sets. (English. Russian original) Zbl 1404.31013
J. Math. Sci., New York 193, No. 1, 55-65 (2013); translation from Zap. Nauchn. Semin. POMI 404 100-119 (2012).
Summary: 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.
MSC:
| 31B15 | Potentials and capacities, extremal length and related notions in higher dimensions |
| 31C15 | Potentials and capacities on other spaces |
References:
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