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- W2020236037 abstract "Take a pair of two disjoint nonpolar compact subsets A and B of the complex plane C = Ĉ{∞}, the complex sphere less the point at infinity, with connected complement Ĉ(A ∪ B) and a simple arc γ in Ĉ(A ∪ B). We form the two sheeted covering surface Ĉγ of Ĉ by pasting Ĉγ with another copy Ĉγ crosswise along γ. Embed A and B in Ĉγ either in the same sheet or in the different sheets and consider the variational 2-capacity cap(A, ĈγB) of A contained in the open subset ĈγB of Ĉγ. Concerning the relation between the above capacity and the variational 2-capacity cap(A, ĈB) of A contained in the open subset ĈB of Ĉ, we will establish the following capacity inequality for the two sheeted cover and its base: 0 < cap (A, ĈγB) < 2 · cap(A, ĈB), where the bound 2 in the above inequality is the best possible in the sense that, for any 0 < τ < 2, there is a triple of A, B, and γ such that cap(A, ĈγB) > τ · cap(A, ĈB), where A and B may in the same sheet or in the different sheets." @default.
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- W2020236037 date "2007-06-01" @default.
- W2020236037 modified "2023-09-27" @default.
- W2020236037 title "Bounds in capacity inequalities for two sheeted spheres" @default.
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- W2020236037 doi "https://doi.org/10.2996/kmj/1183475513" @default.
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