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On smoothness of symmetric mappings II

Author: A. Cantón
Journal: Proc. Amer. Math. Soc. 133 (2005), 103-113
MSC (2000): Primary 30C62; Secondary 30E25
Published electronically: June 2, 2004
MathSciNet review: 2085159
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Abstract: If the dilatation of a quasiconformal selfmap of the upper half-plane vanishes near the real line as a power of the height, the induced quasisymmetric mapping is Lipschitz with the same exponent. In this note, it is shown that the converse does not hold for any positive exponent. In addition, a sufficient condition is found to have locally a quasiconformal extension with the desired growth in the dilatation.

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Additional Information

A. Cantón
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Address at time of publication: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain

Keywords: Quasiconformal mapping, quasisymmetric mapping, Beurling-Ahlfors extension
Received by editor(s): April 16, 2003
Received by editor(s) in revised form: September 4, 2003
Published electronically: June 2, 2004
Additional Notes: The author’s research was supported by an FPI grant from Ministerio de Educación y Cultura (Spain) and a grant from MECD while visiting the University of Washington.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society