Abstract
Generalized capacity of a set and condenser is introduced as a lower bound of the functionalI(v), provided with some symmetrical features where functionv satisfies certain normalizing conditions. It is established that, depending on the type of symmetry of the functionalI(v), the generalized capacity does not increase under such geometric transformations of sets and condensers as polarization, Gonchar standardization, Steinerk-dimensional symmetrization,k-dimensional spherical symmetrization and dissymmetrization. These results strengthen many known statements of this kind for the particular cases of capacities.
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Dubinin, V.N. Capacities and geometric transformations of subsets inn-space. Geometric and Functional Analysis 3, 342–369 (1993). https://doi.org/10.1007/BF01896260
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DOI: https://doi.org/10.1007/BF01896260