Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T23:37:19.514Z Has data issue: false hasContentIssue false
  • English
  • Français

A Property of some Open Riemann Surfaces and Its Application

Published online by Cambridge University Press:  22 January 2016

Tadashi Kuroda
Tadashi Kuroda*
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.

As L. Sario [8] and the others have shown, an important method to investigate the properties of an open Rlemann surface F is the use of an exhaustion of F consisting of compact domains on F. But, for the same purpose, the investigation of properties of a non-compact region on F is also important.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 77 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Ahlfors, L.-Beurling, A.. Conformal invariants and function-theoretic mull-sets,. Acta Math. 83 (1950), pp. 101–129.Google Scholar
[2] Kuroda, T., On the type of an open Riemann surface, Proc. Jap. Acad., 27 (1951), pp. 57–60.Google Scholar
[3] Kuroda, T., Some remarks on an open Riemann surface with null boundary, Tôhoku Math. Journ., (2) 3 (1951), pp. 182–186.Google Scholar
[4] Mori, A., A remark on the class OHD of Riemann surfaces, Kôdai Math. Sem. Rep., (1952), pp. 57–58.Google Scholar
[5] Myrberg, L., Bemerkungen zur Theorie der harmonischen Funktionen, Ann. Acad. Sci. Fenn., A.I. 107 (1952), 8 pp.Google Scholar
[6] Nevanlinna, R., Sur l’existence de certaines classes de différentielles analytiques, C. R. 228 (1949), pp. 2002–2004.Google Scholar
[7] Pfluger, A., Über das Anwachsen eindeutige analytischer Funktionen auf offenen Riemannschen Flächen, Ann. Acad. Sci. Fenn., A.I. 64 (1949), 18 pp.Google Scholar
[8] Sario, L., Über Riemannschen Flache mit hebbarem Rand, Ann. Acad. Sci. Fenn., A.I. 50 (1948), 79 pp.Google Scholar
[9] Tôki, Y., On the classification of open Riemann surfaces, Osaka Math. Journ., 4 (1952), pp. 191–202.Google Scholar
[10] Tsuji, M., Beurling’s theorem on exceptional sets, Tôhoku Math. Journ., (2) 2 (1950), pp. 113–125.Google Scholar
[11] Tsuji, M., Some theorems on open Riemann surfaces, Nagoya Math. Journ., 3 (1951), pp. 141–145.CrossRefGoogle Scholar
[12] Uskila, L., Über die Existenz der beschränkten automorphen Funktionen, Arkiv för Mat., 1 (1949), pp. 1–11.Google Scholar
[13] Ullemar, L., Über die Existenz der automorphen Funktionen mit beschränkten Dirichletintegral, Arkiv för Mat., 2 (1952), pp. 87–97.Google Scholar