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Boundary Components of Riemann Surfaces*

Published online by Cambridge University Press:  22 January 2016

Makoto Ohtsuka
Makoto Ohtsuka*
Affiliation:
Harvard University and Nagoya University
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The boundary components of an abstract Riemann surface were defined by B. v. Kérékjértó [7] and utilized in the book [14] written by S. Stoïlow. It is the purpose of the present paper to investigate their images under conformal mapping and to solve the Dirichlet problem with boundary values distributed on them.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 7 , June 1954 , pp. 65 - 83
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1954

Footnotes

*

This is the work indicated at the footnote 5) of [10]. The essential part of the present paper was first reported to the Annual Meeting of Japanese Mathematical Society held in Tokyo, Japan, in June, 1952, and then to the conference at Michigan, U.S.A., in 1953 (see [11]).

References

[ 1 ] Bieberbach, L.: Lehrbuch der Funktionentheorie, II, Leipzig and Berlin, 1 Aufl. (1927).Google Scholar
[ 2 ] Brelot, M.: Familles de Perron et problème de Dirichlet, Acta Univ. Szeged, 9 (1939), pp. 133–3.Google Scholar
[ 3 ] Brelot, M.: Le problème de Dirichlet “ramifié”, Ann. Grenoble, 22 (1946), pp. 167–0.Google Scholar
[ 4 ] Brelot, M.: Topologies on the boundary and harmonic measures, Proc. Conference on Functions of a Complex Variable, University of Michigan (1953).Google Scholar
[ 5 ] Brelot, M.: and Choquet, G.: Espaces et lignes de Green, Ann. L’Inst. Fourier, 3 (1952), pp. 199–3.CrossRefGoogle Scholar
[ 6 ] Kaila, E.: Über die Ränderzuordnung bei konformer Abbildung von mehrfachzusammen-hängenden Gebieten, Ann. Acad. Sci. Fenn., (A) 55 (1940), No. 9, 63 pp.Google Scholar
[ 7 ] Kérékjártó, B. v.: Vorlesungen über Topologie, Berlin (1923).CrossRefGoogle Scholar
[ 8 ] Ohtsuka, M.: Dirichlet problems on Riemann surfaces and conformal mappings, Nagoya Math. Journ., 3 (1951), pp. 91–7.CrossRefGoogle Scholar
[ 9 ] Ohtsuka, M.: On the behavior of an analytic function about an isolated boundary point, Nagoya Math. Journ., 4 (1952), pp. 103–8.CrossRefGoogle Scholar
[10] Ohtsuka, M.: Note on the harmonic measure of the accessible boundary of a covering Riemann surface, Nagoya Math. Journ., 5 (1953), pp. 35–8.CrossRefGoogle Scholar
[11] Ohtsuka, M.: On boundary components of abstract Riemann surfaces, Proc. Conference on Functions of a Complex Variable, University of Michigan (1953).Google Scholar
[12] Parreau, M.: Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. L’Inst. Fourier, 3 (1952), pp. 103–7.CrossRefGoogle Scholar
[13] Saks, S.: Theory of the integrals, Warsaw (1937).Google Scholar
[14] Stoïlow, S.: Leçons sur les principes topologiques de la théorie des fonctions analytiques, Paris (1938).Google Scholar
[15] Tsuji, M.. Some metrical theorems on Fuchsian groups, Ködai Math. Sem. Report, Nos. 4 – 5(1950), pp. 89–3.Google Scholar