On smoothness of symmetric mappings II

Author:
A. Cantón

Journal:
Proc. Amer. Math. Soc. **133** (2005), 103-113

MSC (2000):
Primary 30C62; Secondary 30E25

DOI:
https://doi.org/10.1090/S0002-9939-04-07498-2

Published electronically:
June 2, 2004

MathSciNet review:
2085159

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Abstract | References | Similar Articles | Additional Information

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

Email:
acanton@mat.uab.es

DOI:
https://doi.org/10.1090/S0002-9939-04-07498-2

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