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On a Ring Isomorphism Induced by Quasiconformal Mappings

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Mathematical Institute, Nagoya University
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The purpose of this paper is to study the relationship between a certain isomorphism of some rings of functions on Riemann surfaces and a quasi-conformal mapping.

It is well known that two compact Hausdorff spaces are topologically equivalent if and only if their rings of continuous functions are isomorphic. We shall establish an analougous result concerning a function ring on a Riemann surface and the quasi-conformal equivalence.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 14 , February 1959 , pp. 201 - 221
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[ 1 ] Ahlfors, L., On quasi-conformal mapping, Journal d’ Analyse Mathématique, vol. 3 (1953/4), 1–58, 207–208.CrossRefGoogle Scholar
[ 2 ] Bers, L., On a theorem of Mori and the definition of quasi-conformality, Trans. Amer. Math. Soc, vol. 84 (1957), 78–84.Google Scholar
[ 3 ] Bourbaki, N., Intégration, chap. III, § 4.Google Scholar
[ 4 ] Loomis, L., An introduction to abstract harmonic analysis, 1953.Google Scholar
[ 5 ] Mori, A., On quasi-conformality and pseudo-analiticity, Trans. Amer. Math. Soc, vol. 85 (1957), 56–77.Google Scholar
[ 6 ] Mori, S., A remark on a subdomain of a Riemann surface of the class OHD, Proc. Japan Acad., vol. 32 (1958), 251–254.Google Scholar
[ 7 ] Mori, S. and Ota, M., A remark on the ideal boundary of a Riemann surface, Proc. Japan Acad., 32, No. 6 (1956). 409–411.Google Scholar
[ 8 ] Pfluger, A., Sur un propriété de l’application quasi conforme d’une surface de Riemann ouverte, C. R. Acad. Sci. Paris, vol. 227 (1948), 25–26.Google Scholar
[ 9 ] Royden, H.L., Harmonic functions on open Riemann surface, Trans. Amer. Math. Soc, vol. 73 (1952), 40–94.CrossRefGoogle Scholar
[10] Royden, H.L., The ideal boundary of an open Riemann surface, Annals of Mathematics Studies, No. 30 (1953), 107–109.Google Scholar
[11] Royen, H.L., A property of quasi-conformal mapping, Proc. Amer. Math. Soc, vol. 85 (1954), 266–269.Google Scholar
[12] Yûjôbô, Z., On absolutely continuous functions of two or more variables in the Tonelli sense and quasi-conformal mappings in the A. Mori sense, Comment. Math. Univ. St. Pauli, Tome IV (1955), 67–92.Google Scholar