A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

We give a short new proof that for each non-elementary Kleinian group Γ , the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of Γ , and that strict inequality holds if Γ is of divergence type.

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Bibliographische Detailangaben
Veröffentlicht in:	The Journal of Geometric Analysis 2015-01, Vol.25 (1), p.298-305
1. Verfasser:	Jaerisch, Johannes
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Beschreibung
Zusammenfassung:	We give a short new proof that for each non-elementary Kleinian group Γ , the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of Γ , and that strict inequality holds if Γ is of divergence type.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-013-9427-4