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Equality of the capacity and module of a condenser on a surface. (English. Russian original) Zbl 1066.31005
J. Math. Sci., New York 118, No. 1, 4795-4807 (2003); translation from Zap. Nauchn. Semin. POMI 276, 112-133 (2001).
Summary: We study properties of the capacity of a condenser and of the module of a family of curves on a surface. Some properties of the spaces \(L_{\varphi,F}(G)\) and \(L_{\varphi,F}^1(G)\) are established. These properties are applied in proving that the capacity and module of a capacity on a surface are equal.

MSC:
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
31C15 Potentials and capacities on other spaces
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