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Green Potential of Evans Type on Royden’s Compactification of a Riemann Surface

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Mathematical Institute, Nagoya University
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Let R be a hyperbolic Riemann surface and gw(z) be the Green function on R with its pole w in R. We denote by (R) the totality of sequences of points in R not accumulating in R and

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 24 , June 1964 , pp. 205 - 239
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1964

References

[1] Cornea, C. Constantinescu-A.: Ideale Ränder Riemannscher Flächen, Springer-Verlag, 1963.Google Scholar
[2] Evans, G. C.: Potentials and positively infinite singularites of harmonic functions, Monatsheft für Math, und Phys., 43 (1936), 419–424.CrossRefGoogle Scholar
[3] Kuramochi, Z. : Mass distributions on the ideal boundaries of abstract Riemann surfaces, I, Osaka Math. J., 8 (1956), 119–137.Google Scholar
[4] Kusunoki, Y.-S. Mori: On the harmonic boundary of an open Riemann surface, I, Japanese J. Math., 29 (1960), 52–56.CrossRefGoogle Scholar
[5] Nakai, M. : On a ring isomorphism induced by quasicoformal mappings, Nagoya Math. J., 14 (1959), 201–221.Google Scholar
[6] Nakai, M. : A measure on the harmonic boundary of a Riemann surface, Nagoya Math. J., 17 (1960), 181–218.CrossRefGoogle Scholar
[7] Nakai, M. : Genus and classification of Riemann surfaces, Osaka Math. J., 14 (1962), 153–180.Google Scholar
[8] Nakai, M. : On Evans potential, Proc. Japan Acad., 38 (1962), 624–629.Google Scholar
[9] Nakai, M. : Evans’ harmonic function on Riemann surfaces, Proc. Japan Acad., 39 (1963), 74–78.Google Scholar
[10] Nakai, M. : On Evans’ solution of the equation Δu = Pu on Riemann surfaces, Kôdai Math. Sem. Rep., 15 (1963), 79–93.Google Scholar
[11] Ninomiya, N.: Etude sur la théorie du potential pris par rapport au noyau symétrique, J. Inst. Polytech. Osaka City Univ., 8 (1957), 147–179.Google Scholar
[12] Noshiro, K.: Contributions to the theory of singularities of analytic functions, Japanese J. Math., 19 (1948), 299–327.Google Scholar
[13] Sario, L.: A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Soc Math., 72 (1952), 281–295.Google Scholar
[14] Selberg, H.: Über die ebenen Punktmengen von der Kapazitât Null, Avh. Norske Videnskaps-Acad. Oslo I Math.-Natur, 10 (1937).Google Scholar