On the proper conjugation of Kleinian groups
In the paper under review the authors studies geometrically finite Kleinian groups acting isometrically on the hyperbolic space \(\mathbb{H}^n\). The main result of the paper is the following: Theorem. Suppose \(K \in Iso \mathbb{H}^n\) is a geometrically finite nonelementary Kleinian group or an elementary Kleinian group with two fixed points at infinity, and \(g \in Iso \mathbb{H}^n\) is a Möbius transformation. Then \(gKg^{-1} \subset K\) implies that \(gKg^{-1} = K\). Reviewer's remark. The proof of the theorem stated for the whole isometry group \(Iso \mathbb{H}^n\) of the hyperbolic space \(H^n\), is given only for its orientation preserving part \(Iso_+ \mathbb{H}^n\).
scientific article; zbMATH DE number 806252