an:00902734
Zbl 0851.30008
Ghamsari, Manouchehr
Quasiconformal groups acting on \(B^ 3\) that are not quasiconformally conjugate to M??bius groups
EN
Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 2, 245-250 (1995).
00034640
1995
j
30C62 30C65
quasiconformal group
It is shown that there is a quasiconformal group acting on the unit ball of \(\mathbb{R}^3\) which is not quasiconformally conjugate to any M??bius group. The construction is based on Tukia's idea on the rigidity of quasiconformal maps in this context [\textit{P. Tukia}, Ann. Acad. Sci. Fenn., Ser. A I 6, 149-160 (1981; Zbl 0473.30015)]. In the plane the situation is different (Sullivan, Tukia). For \(n\geq 4\) there exist simpler constructions [\textit{G. Martin}, Ann. Acad. Sci. Fenn., Ser. A I 11, 179-202 (1986; Zbl 0635.30021)], [\textit{O. Martio} and \textit{J. V??is??l??}, Math. Ann. 282, No. 3, 423-443 (1988; Zbl 0632.35021)].
O.Martio (Helsinki)
Zbl 0473.30015; Zbl 0635.30021; Zbl 0632.35021