A note on the construction of a certain class of Kleinian groups
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- by Ricardo Bianconi PDF
- Proc. Amer. Math. Soc. 123 (1995), 3119-3124 Request permission
Abstract:
We prove that if $\{ {S_1},{S_1}’, \ldots ,{S_n},S_n’\}$ is a collection of distinct spheres in ${\mathbb {R}^m}$ with common exterior, and ${g_1}, \ldots ,{g_n}$ are Möbius transformations such that for each i, ${S_i}$ is the isometric sphere of ${g_i}$ and $S_i’$ is the isometric sphere of $g_i^{ - 1}$ and such that ${g_i}$ maps points of contact of ${S_i}$, to points of contact of $S_i’$, then the group G generated by the ${g_i}$’s is Kleinian.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3119-3124
- MSC: Primary 30F40; Secondary 20H10
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277097-0
- MathSciNet review: 1277097