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 S n \textbf {S}^{n} , n > 0 n>0 , is a quasisymmetric conjugate of a Möbius group that acts on S n \textbf {S}^{n} . This was shown to be true for n = 2 n=2 by Sullivan and Tukia, and it was shown to be wrong for n > 2 n>2 by Tukia. It also follows from the work of Martin and of Freedman and Skora. In this paper we settle the case of n = 1 n=1 by showing that any K K -quasisymmetric group is K 1 K_1 -quasisymmetrically conjugated to a Möbius group. The constant K 1 K_1 is a function K K .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Journal of the American Mathematical Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
