A lower estimate of the sum of the capacities of condensers
type: Item
instance of: scholarly article
title: A lower estimate of the sum of the capacities of condensers
zbMATH Open document ID: 0707.31003
DOI: 10.1007/BF01057022
author: I. P. Mityuk
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The main result is contained in a theorem asserting the inequality \(\sum^{n}_{k=1}| A_ k| \geq \sum^{n}_{k=1}| C_ k|\), where \(| A_ k|\) is the capacity of the condenser \(A_ k\) with the potential function \(\omega (z,A_ k)\) and \(| C_ k|\) is the capacity of the condenser \(C^ n_ k=\{\dot G^ n_ k,E_{\ell}\}\); \(\dot G^ n_ k\) is the convex component of the set \(G^ n_ k\) in the neighbourhood of \(E_{\ell}\). This inequality could be extended to condensers with compact sets having transfinite diameter.
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 4161086
zbMATH Keywords: capacity
zbMATH Keywords: condenser
MaRDI profile type: Publication
cites work: An inequality for logarithmic capacities
cites work: Estimates for the transfinite diameter with applications to conformal mapping
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description: scientific article; zbMATH DE number 4161086