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A New Definition of the n-Dimensional Quasiconformal Mappings

Published online by Cambridge University Press:  22 January 2016

Petru Caraman
Petru Caraman*
Affiliation:
Mathematical Institute, Roumanian Acadenuy, Iasi
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In this note we shall extend, for arbitrary n, Pesin’s [11] bidimensional definition for quasiconformal mappings and establish its equivalence with Gehring’s [7] and Väisälä’s [15] definitions.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 26 , February 1966 , pp. 145 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bouligand, G., Introduction à la geometrie infinitesimale directe. Paris, 1932.Google Scholar
[2] Caraman, P. P., Contribution à la theorie des representations quasi-conformes n-dimensionnelles. Revue de Math. Pures et Appl., 6 (1961), 311–356.Google Scholar
[3] Caraman, P. P., Quelques proprietes des representations quasi conformes de En I, II. Revue de Math. Pures et Appl., 1964 (to appear).Google Scholar
[4] Chén, Hàng-lén, Quasiconformal mappings in n-dimensional space. Chinese. Acta Math. Sinica, 14 (1964), 93–102.Google Scholar
[5] Fuglede, B., Extremal length and functional completion. Acta Math., 98 (1957), 171–219.Google Scholar
[6] Gehring, F. W., Extremal length definitions for the conformal capacity in space. Michigan Math. J., 9 (1962), 137–150.Google Scholar
[7] Gehring, F. W., Rings and quasi conformal mappings in space. Trans. AMS, 103 (1962), 353–393.Google Scholar
[8] Krivov, V. V., Some modulus properties in space. Russian. Dokl. Akad. Nauk. SSSR, (1964), 510–513.Google Scholar
[9] Loewner, C., On conformal capacity in space. J. Math. Mech., 8 (1959), 411–414.Google Scholar
[10] Markuševič, H. I., On some classes of continuous mappings. Russian. Dokl. Akad. Nauk SSSR, 28 (1940), 301–304.Google Scholar
[11] Pesin, I. I., Metric properties of Q-quasiconformal mappings. Russian. Mat. Sb., 40 (1956), 281–294.Google Scholar
[12] Rado, T. and Reichelderfer, P. V., Continuous transformations in analysis. Berlin-Göttingen-Heidelberg, 1955.Google Scholar
[13] Roger, F., Sur la relation entre les propriétés tangentielles et metriques des ensembles cartesiens. C. R. Acad. Sci. Paris, 201 (1935), 871–873.Google Scholar
[14] Saks, S., Theory of integral. New York, 1937.Google Scholar
[15] Väisälä, J., On quasiconformal mappings in space. Ann. Acad. Sci. Fenn. Ser. A, I, 298 (1961), 1–36.Google Scholar