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Superharmonic Functions in a Domain of a Riemann Surface

Published online by Cambridge University Press:  22 January 2016

Zenjiro Kuramochi
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 41 - 55
Copyright
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
[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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[8] See [2].Google Scholar