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Behaviour of Green Lines at Royden’s Boundary of Riemann Surfaces

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Mathematical Institute, Nagoya University
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The aim of this paper is to investigate the behaviour of Green lines at Royden’s boundary Γ of a Riemann surface R with the Green function g(z, o) with the fixed pole o in R. We denote by the totality of Green lines L issuing from the fixed point o.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 24 , June 1964 , pp. 1 - 27
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1964

References

[1] Constantinescu, C. and Cornea, A.: Über den idealen Rand und einige seiner Anwendungen bei der Klassifikation der Riemannschen Flächen, Nagoya Math. J., 13 (1958), 169–233.Google Scholar
[2] Brelot, M. et Choquet, G.: Espaces et lignes de Green, Ann. Inst. Fourier, 3 (1951), 119–263.Google Scholar
[3] Godefroid, M.: Une propriété des fonctions B.L.D. dans un espace de Green, Ann. Inst. Fourier, 9 (1959), 301–304.Google Scholar
[4] Kusunoki, Y. and Mori, S.: On the harmonic boundary of an open Riemann surface, Jap. J. Math., 29 (1960), 52–56.Google Scholar
[5] Nakai, M.: On a ring isomorphism induced by quasiconformal 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.Google Scholar
[7] Nakai, M.: Bordered Riemann surface with parabolic double, Proc. Japan Acad., 37 (1961), 553–555.Google Scholar
[8] Nakai, M.: Genus and classification of Riemann surfaces, Osaka Math. J., 14 (1962), 153–180.Google Scholar
[9] Royden, H. L.: The ideal boundary of an open Rimann surface, Ann. Math. Studies, 30 (1953), 107–109.Google Scholar