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Conformal mapping and ellipses

Author(s): Arne Ledet; Alexander Yu. Solynin
Journal: Proc. Amer. Math. Soc. 134 (2006), 3507-3513.
MSC (2000): Primary 30C35
Posted: June 27, 2006
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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:

1.: M. Chuaqui, P. Duren, and B. Osgood, Ellipses, near ellipses, and harmonic Möbius transformations. Proc. Amer. Math. Soc., 133 (2005), no. 9, 2705-2710. MR 2146217 (2005m:31002)
2.: J. A. Jenkins, Univalent functions and conformal mapping, 2nd ed. Springer, Berlin, 1965. MR 0096806 (20:3288)
3.: B. L. van der Waerden, Algebra. Vol. I. Springer-Verlag, New York, 1991. MR 1080172 (91h:00009a)

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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
Email: alex.solynin@ttu.edu

DOI: 10.1090/S0002-9939-06-08482-6
PII: S 0002-9939(06)08482-6
Keywords: Conformal mapping, ellipse
Received by editor(s): June 6, 2005
Posted: 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 of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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