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Ellipses, near ellipses, and harmonic Möbius transformations

Author(s): Martin Chuaqui; Peter Duren; Brad Osgood
Journal: Proc. Amer. Math. Soc. 133 (2005), 2705-2710.
MSC (2000): Primary 30C99; Secondary 31A05
Posted: March 22, 2005
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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.

References:

1.: M. Chuaqui, P. Duren, and B. Osgood, The Schwarzian derivative for harmonic mappings, J. Analyse Math. 91 (2003), 329-351. MR 2037413 (2004j:30030)
2.: P. Duren, Harmonic Mappings in the Plane, Cambridge University Press, Cambridge, U.K., 2004. MR 2048384

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Additional Information:

Martin Chuaqui
Affiliation: Facultad de Matemáticas, P. Universidad Católica de Chile, Santiago, Chile
Email: mchuaqui@mat.puc.cl

Peter Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109--1109
Email: duren@umich.edu

Brad Osgood
Affiliation: Department of Electrical Engineering, Stanford University, Stanford, California 94305
Email: osgood@stanford.edu

DOI: 10.1090/S0002-9939-05-07817-2
PII: S 0002-9939(05)07817-2
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
Posted: March 22, 2005
Additional Notes: The first author was supported by Fondecyt Grant # 1030589
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2005, American Mathematical Society


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