Geometriae Dedicata

, Volume 125, Issue 1, pp 63–74 | Cite as

Critical exponents for groups of isometries

  • Richard SharpEmail author
Original Paper


Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ / Γ0 is amenable.


CAT(−1)space Riemannian manifold Negative curvature Group of isometrics Critical exponent Amenable group 

Mathematics Subject Classifications (2000)

20F67 20F69 37C35 60B99 


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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterU.K.

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