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Circle Means of Green’s Functions

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Nagoya University
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Consider the polar coordinate differentials (dr, dθ) on a hyperbolic Riemann surface R with center z0 ∈ R which are given by

where GR(z, ζ) is the Green’s function on R with pole ζ ∈ R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 49 , March 1973 , pp. 1 - 7
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Brelot, M.-Choquet, G.: Espaces et lignes de Green, Ann. Inst. Fourier 3 (1951), 199–263.Google Scholar
[2] Kuramochi, Z.: Harmonic measures and capacity of sets of the ideal boundary. II, Proc. Japan Acad., 32 (1955), 25–30.Google Scholar
[3] Kusunoki—, Y. Mori, S.: On the harmonic boundary of an open Riemann surface, Japan. J. Math., 24 (1960), 52–56.Google Scholar
[4] Nakai, M.: Bordered Riemann surface with parabolic double, Proc. Japan Acad., 37 (1961), 553–555.Google Scholar
[5] Nakai, M.: Behaviour of Green lines at Royden’s boundary of Riemann surfaces, Nagoya Math. J., 24 (1964), 1–27.Google Scholar
[6] Sario—, L. Nakai, M.: Classification Theory of Riemann Surfaces, Springer, 1970.Google Scholar