Discrete quasiconformal groups with small dilatation (Q2640721)

The author proves that, for each \(n\geq 2\) and each \(K>1\), there is a K- quasiconformal, non-elementary discrete group acting on the one-point compactification of n-dimensional Euclidean space (that is, on the n- sphere) which is not the quasiconformal conjugate of any Möbius group. This result completes a series of results in the same vein by Tukia, Martin, Gehring, and Martin, Freedman and Skora, and the author. The added conclusion in the present case is that the dilatation can be required to be as near 1 as desired.