an:01428728
Zbl 0945.30035
Bonfert-Taylor, Petra
J??rgensen's inequality for discrete convergence groups
EN
Ann. Acad. Sci. Fenn., Math. 25, No. 1, 131-150 (2000).
00061260
2000
j
30F40 57S30 30C62 20H10
convergence groups; quasiconformal groups; Kleinian groups; J??rgensen's inequality
We explore in this paper whether certain fundamental properties of the action of Kleinian groups on the Riemann sphere extend to the action of discrete convergence groups on \(\overline{\mathbf R^2}\). A J??rgensen inequality for discrete \(K\)-quasiconformal groups is developed, and it is shown that such an inequality depends naturally on the quasiconformal dilatation \(K\). Furthermore, it is established that no such inequality can hold for general discrete convergence groups. In the discontinuous case a universal constraint on discreteness is formulated for both quasiconformal and general convergence groups.