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Conformal mapping and ellipses
Authors:
Arne Ledet and Alexander Yu. Solynin
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3507-3513
MSC (2000):
Primary 30C35
Posted:
June 27, 2006
MathSciNet review:
2240662
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Abstract |
References |
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Additional Information
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:
http://dx.doi.org/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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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