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On the Behaviour of Analytic Functions in the Neighbourhood of the Boundary of a Riemann Surface

Published online by Cambridge University Press:  22 January 2016

A. Cornea
A. Cornea*
Affiliation:
Institute of Mathematics, Academy R.P.R.Bucarest
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Mr. Z. Kuramochi has recently obtained the following very interesting result concerning the classification of Riemann surfaces [1]:

If we delete from a Riemann surface belonging to the class an arbitrary compact set, the resulting surface remains in the class .

In the present paper we indicate a new method of proving this theorem, simultaneously for the cases B and D.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 55 - 58
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Kuramochi, Z., On the behaviour of analytic functions on abstract Riemann surfaces, Osaka Math. J., vol. 7, nr. 1 (1955), pp. 109–127.Google Scholar
[2] Sario, L., A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Math. Soc, vol. 72(1952), pp. 281–295.Google Scholar
[3] Nevanlinna, R., Uniformisierung, Springer Verlag, Berlin (1953), pp. 320–328.Google Scholar
[4] Parreau, M., Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier, vol. 3(1952), pp. 103–197.Google Scholar