Journal of the American Mathematical Society

Author(s): Vladimir Markovic
Journal: J. Amer. Math. Soc. 19 (2006), 673-715.
MSC (2000): Primary 20H10, 37F30
Posted: January 25, 2006
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Abstract: One of the first problems in the theory of quasisymmetric and convergence groups was to investigate whether every quasisymmetric group that acts on the sphere ${\bf S}^{n}$ ,

, is a quasisymmetric conjugate of a Möbius group that acts on ${\bf S}^{n}$ . This was shown to be true for

by Sullivan and Tukia, and it was shown to be wrong for

by Tukia. It also follows from the work of Martin and of Freedman and Skora. In this paper we settle the case of

by showing that any

-quasisymmetric group is

-quasisymmetrically conjugated to a Möbius group. The constant

is a function

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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 20H10, 37F30

Vladimir Markovic
Affiliation: University of Warwick, Institute of Mathematics, Coventry CV4 7AL, United Kingdom
Email: markovic@maths.warwick.ac.uk

DOI: 10.1090/S0894-0347-06-00518-2
PII: S 0894-0347(06)00518-2
Received by editor(s): December 15, 2004
Posted: January 25, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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