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On the Denjoy Conjecture

Published online by Cambridge University Press:  20 November 2018

James A. Jenkins
James A. Jenkins*
Affiliation:
University of Notre Dame
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In recent years many of the properties of regular functions have been shown to extend to quasiconformal mappings. (The latter term is here understood in the sense defined in (5).) This is particularly true of those results which can be proved by use of the method of the extremal metric. It is rather strange, then, that a result which constitutes one of the first notable applications of this method has not been so extended (at least to the author's knowledge).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 627 - 631
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Ahlfors, Lars V., Untersuchungen zur Theorie der konformen Abbildung und der ganzen Funktionen, Acta Societatis Scientiarum Fennicae, Nova Series A, Opera Phys.-math., 1, (1930), no. 9, 1-40.Google Scholar
2. Beurling, A., Etudes sur un problème de majoration, thesis (Upsala, 1933).Google Scholar
3. Carleman, T., Sur une inégalité différentielle dans la théorie des fonctions analytiques, C. R. Acad. Sci. Paris, 196 (1933), 995-997.Google Scholar
4. Jenkins, James A., Symmetrization results for some conformai invariants, Amer. J. Math., 75 (1953), 510-522.Google Scholar
5. Jenkins, James A., On quasiconformal mappings, J. Rat. Mech. and Anal., 5 (1956), 343-352.Google Scholar
6. Jenkins, James A., Univalent functions and conformai mapping, No. 18, Ergebnisse der Mathematik, Springer-Verlag (to appear).Google Scholar