Ellipses, near ellipses, and harmonic Möbius transformations
HTML articles powered by AMS MathViewer
- by Martin Chuaqui, Peter Duren and Brad Osgood PDF
- Proc. Amer. Math. Soc. 133 (2005), 2705-2710 Request permission
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
- Martin Chuaqui, Peter Duren, and Brad Osgood, The Schwarzian derivative for harmonic mappings, J. Anal. Math. 91 (2003), 329–351. MR 2037413, DOI 10.1007/BF02788793
- Peter Duren, Harmonic mappings in the plane, Cambridge Tracts in Mathematics, vol. 156, Cambridge University Press, Cambridge, 2004. MR 2048384, DOI 10.1017/CBO9780511546600
Additional Information
- Martin Chuaqui
- Affiliation: Facultad de Matemáticas, P. Universidad Católica de Chile, Santiago, Chile
- MR Author ID: 319580
- 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
- MR Author ID: 134465
- Email: osgood@stanford.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2705-2710
- MSC (2000): Primary 30C99; Secondary 31A05
- DOI: https://doi.org/10.1090/S0002-9939-05-07817-2
- MathSciNet review: 2146217