On a Ring Isomorphism Induced by Quasiconformal Mappings
- 1 February 1959
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 14, 201-221
- https://doi.org/10.1017/s0027763000005857
Abstract
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.Keywords
This publication has 6 references indexed in Scilit:
- A remark on a subdomain of a Riemann surface of the class $O_HD$Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1958
- On a theorem of Mori and the definition of quasiconformalityTransactions of the American Mathematical Society, 1957
- On quasi-conformality and pseudo-analyticityTransactions of the American Mathematical Society, 1957
- A Riemann on the ideal boundary of a Riemann surfaceProceedings of the Japan Academy, Series A, Mathematical Sciences, 1956
- Correction to “On quasiconformal mappings”Journal d'Analyse Mathématique, 1953
- Harmonic functions on open Riemann surfacesTransactions of the American Mathematical Society, 1952