Wensheng Cao
Articles written in Proceedings – Mathematical Sciences
Volume 123 Issue 2 May 2013 pp 245-251
Notes on Discrete Subgroups of Möbius Transformations
Hua Wang Yueping Jiang Wensheng Cao
Jørgensen’s inequality gives a necessary condition for a nonelementary two generator subgroup of $SL(2,\mathbb{C})$ to be discrete. By embedding $SL(2,\mathbb{C})$ into $Û(1,1;\mathbb{H})$, we obtain a new type of Jørgensen’s inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this result gives an improvement over the classical Jørgensen’s inequality.
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