Conformal mapping and ellipses
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- by Arne Ledet and Alexander Yu. Solynin PDF
- Proc. Amer. Math. Soc. 134 (2006), 3507-3513 Request permission
Abstract:
We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses.References
- Martin Chuaqui, Peter Duren, and Brad Osgood, Ellipses, near ellipses, and harmonic Möbius transformations, Proc. Amer. Math. Soc. 133 (2005), no. 9, 2705–2710. MR 2146217, DOI 10.1090/S0002-9939-05-07817-2
- James A. Jenkins, Univalent functions and conformal mapping, Reihe: Moderne Funktionentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0096806
- B. L. van der Waerden, Algebra. Vol. I, Springer-Verlag, New York, 1991. Based in part on lectures by E. Artin and E. Noether; Translated from the seventh German edition by Fred Blum and John R. Schulenberger. MR 1080172, DOI 10.1007/978-1-4612-4420-2
Additional Information
- Arne Ledet
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
- Email: arne.ledet@ttu.edu
- Alexander Yu. Solynin
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
- MR Author ID: 206458
- Email: alex.solynin@ttu.edu
- Received by editor(s): June 6, 2005
- Published electronically: June 27, 2006
- Additional Notes: The research of the second author was supported in part by NSF grant DMS-0412908
- Communicated by: Juha M. Heinonen
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3507-3513
- MSC (2000): Primary 30C35
- DOI: https://doi.org/10.1090/S0002-9939-06-08482-6
- MathSciNet review: 2240662