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On a Type Problem

Published online by Cambridge University Press:  20 November 2018

James A. Jenkins
James A. Jenkins*
Affiliation:
University of Notre Dame Institute for Advanced Study
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Considerable interest has attached to the problem of determining the type of a Riemann surface obtained by performing an identification between the edges of a strip or a half-strip (1, 2, 4, 5, 8). A fairly thorough analysis was made in 1946 by Volkovyskii (6) who gave various sufficient conditions for parabolic and hyperbolic type. The object of the present paper is to show that his principal sufficient condition for hyperbolic type can be substantially improved.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 427 - 431
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Blanc, C., Les surfaces de Riemann des fonctions méromorphes, Comm. Math. Helvet., 9 (1936-7), 193–216, 335-68.Google Scholar
2. Blanc, C., Les demi-surfaces de Riemann. Application au problème du type, Comm. Math. Helvet., 10 (1938-9), 130-50.Google Scholar
3. Jenkins, James A., Univalent functions and conformai mapping (Springer-Verlag, Berlin- Göttingen-Heidelberg, 1958).Google Scholar
4. Nevanlinna, R., Ueber die Polygondarstellung einer Riemannschen Fläche, Ann. Acad. Sci. Fenn. Ser. AI, no. 122 (1952).Google Scholar
5. Nevanlinna, R., “Polygonal representation of Riemann surfaces,” Lectures on functions of a complex variable (Michigan, 1955), 65–70.Google Scholar
6. Volkovyskii, L. I., On the problem of type of simply-connected Riemann surfaces, Mat. Sbornik, 18 (N.S.) (1946), 185–211 (Russian, English summary).Google Scholar
7. Volkovyskii, L. I., Quasiconformal mapping and the problem of conformai pasting, Ukrain. Mat. Z., 3 (1951), 39–52 (Russian).Google Scholar
8. Wirth, E. M., Ueber die Bestimmung des Typus einer Riemannschen Fläche, Comm. Math. Helvet., 31 (1956), 90–107.Google Scholar