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Superharmonic Functions in a Domain of a Riemann Surface
Published online by Cambridge University Press: 22 January 2016
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Let R be a Riemann surface. Let G be a domain in R with relative boundary ∂G of positive capacity. Let U(z) be a positive superharmonic function in G such that the Dirichlet integral D(min(M,U(z))) < ∞ for every M. Let D be a compact domain in G.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1968
References
[1] If ∂G and ∂D are compact and smooth, d(λ,z) is given as 
where N(ζ,z) is the N-Green’s function of G – D with pole at z.Google Scholar
where N(ζ,z) is the N-Green’s function of G – D with pole at z.Google Scholar[2]
Kuramochi, Z.: Potentials on Riemann surfaces. Journ. Fac. Sci. Hokkaido Uni., XVI (1962). See page 14 of this paper.Google Scholar
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