Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T06:38:51.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytic Functions on Some Riemann Surfaces, II

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In their paper [12], Toda and the author have concerned themselves in the following

Theorem of Kuramochi. Let R be a hyperbolic Riemann surface of the class OHB(OHD, resp.). Then, for any compact subset K of R such that R−K is connected, R−K as an open Riemann surface belongs to the class OAB(OAD, resp.) (Kuramochi [4]).

They have raised there the question as to whether there exists a hyperbolic Riemann surface, which has no Martin or Royden boundary point with positive harmonic measure and has yet the same property as stated in Theorem of Kuramochi, and given a positive answer to the Martin part of this question.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 23 , December 1963 , pp. 153 - 164
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

[1] Constantinescu, C. and Cornea, A.: Über den idealen Rand und einige seiner Anwendungen bei Klassifikation der Riemannschen Flächen, Nagoya Math. J. 13 (1958), 166–233.CrossRefGoogle Scholar
[2] Heins, M.: On the Lindelöfian principle, Ann. of Math. 61 (1955), 440–473.CrossRefGoogle Scholar
[3] Kuramochi, Z.: Relations between harmonic dimensions, Proc. Japan Acad. 30 (1954), 576–580.Google Scholar
[4] Kuramochi, Z.: On the behaviour of analytic functions on abstract Riemann surfaces, Osaka Math. J. 7 (1955), 109–127.Google Scholar
[5] Kuramochi, Z.: Representation of Riemann surfaces, Osaka Math. J. 11 (1959), 71–82.Google Scholar
[6] Kuroda, T.: On some theorems of Sario, Bull. Math. Soc. Sci. Math. Phys. R.P.R. 2 (50) (1958), 411–417.Google Scholar
[7] Kusunoki, Y. and Mori, S.: On the harmonic boundary of an open Riemann surface, II, Mem. Coll. Sci. Univ. Kyoto 33 (1960), 209–223.Google Scholar
[8] Matsumoto, K.: On subsurfaces of some Riemann surfaces, Nagoya Math. J. 15 (1959), 261–274.CrossRefGoogle Scholar
[9] Nakai, M.: A measure on the harmonic boundary of a Riemann surface, Nagoya Math. J. 17 (1960), 181–218.CrossRefGoogle Scholar
[10] Nakai, M.: Genus and classification of Riemann surfaces, Osaka Math. J. 14 (1962), 153–180.Google Scholar
[11] Noshiro, K.: Cluster Sets, Berlin (1960).Google Scholar
[12] Toda, N. and Matsumoto, K.: Analytic functions on some Riemann surfaces, Nagoya Math. J. 22 (1963), 211–217.CrossRefGoogle Scholar