Generalized capacities, compound curves and removable sets
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 100-119
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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.
@article{ZNSL_2012_404_a5,
author = {Yu. V. Dymchenko and V. A. Shlyk},
title = {Generalized capacities, compound curves and removable sets},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {100--119},
publisher = {mathdoc},
volume = {404},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a5/}
}
Yu. V. Dymchenko; V. A. Shlyk. Generalized capacities, compound curves and removable sets. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 100-119. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a5/