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Relative Distance and Quasi-Conformal Mappings

Published online by Cambridge University Press:  22 January 2016

D. A. Storvick
D. A. Storvick*
Affiliation:
Department of Mathematics, University of Minnesota
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1. Introduction. M. A. Lavrentiev made use of a relative distance function to establish some important results concerning the correspondence between the frontiers under a conformal mapping of a simply connected domain onto the unit circle. The purpose of this note is to show that some of these results are valid for the boundary correspondences induced by the more general class of quasi-conformal mappings.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 111 - 117
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Ahlfors, L., On quasi-conformal mappings, Journal d’Analyse Mathématique, 3 (1953/54), 1–58.CrossRefGoogle Scholar
[2] Beurling, A., Ensemble exceptionnels, Acta Math., 72 (1940), 1–13.Google Scholar
[3] Koebe, P., Abhandlungen zur Theorie der konformen Abbildung I, J. f. reine u. angew. Math., 145 (1915), 177–223.CrossRefGoogle Scholar
[4] Lavrentiev, M., Sur la représentation conforme, C. R. Acad. Sci. Paris, 184 (1927), 1407–1409.Google Scholar
[5] Lavrentiev, M., Sur la correspondence entre les frontières dans la représentation conforme, Rec. Math., 36 (1929), 112–115.Google Scholar
[6] Mori, A., On quasi-conformality and pseudo-analyticity, Trans. Amer. Math. Soc., 84 (1957), 56–77.CrossRefGoogle Scholar
[7] Tôki, Y. and Shibata, K., On the pseudo-analytic functions, Osaka Math. J., 6 (1954), 145–165.Google Scholar