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A generalization of the Shimizu-Leutbecher and Jørgensen inequalities to Möbius transformations in \({\mathbb{R}}^ N\). (English) Zbl 0812.30017
In this well written and well documented short paper, the author obtains a generalization of the Shimizu-Leutbecher inequality and a partial generalization of the Jørgensen inequality in the theory of Kleinian groups to Möbius transformations in \(\mathbb{R}^ N\). Methods include use of the Clifford algebra and the Vahlen group.

MSC:
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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