Dymchenko, Yu. V. 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. Cited in 3 Documents MSC: 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 31C15 Potentials and capacities on other spaces Keywords:extremal functions; Borel function; Clarkson inequality PDF BibTeX XML Cite \textit{Yu. V. Dymchenko}, J. Math. Sci., New York 118, No. 1, 4795--4807 (2001; Zbl 1066.31005); translation from Zap. Nauchn. Semin. POMI 276, 112--133 (2001) Full Text: DOI