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Ellipses, near ellipses, and harmonic Möbius transformations

Authors: Martin Chuaqui, Peter Duren and Brad Osgood
Journal: Proc. Amer. Math. Soc. 133 (2005), 2705-2710
MSC (2000): Primary 30C99; Secondary 31A05
Published electronically: March 22, 2005
MathSciNet review: 2146217
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Abstract: It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation.

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Additional Information

Martin Chuaqui
Affiliation: Facultad de Matemáticas, P. Universidad Católica de Chile, Santiago, Chile

Peter Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109

Brad Osgood
Affiliation: Department of Electrical Engineering, Stanford University, Stanford, California 94305

Keywords: Harmonic mapping, Schwarzian derivative, harmonic M\"{o}bius transformation, circles, ellipses
Received by editor(s): January 22, 2004
Received by editor(s) in revised form: April 29, 2004
Published electronically: March 22, 2005
Additional Notes: The first author was supported by Fondecyt Grant # 1030589
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2005 American Mathematical Society