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Continuity of critical exponent of quasiconvex-cocompact groups under Gromov–Hausdorff convergence

Part of: Global differential geometry Special aspects of infinite or finite groups

Published online by Cambridge University Press:  10 February 2022

NICOLA CAVALLUCCI Open the ORCID record for NICOLA CAVALLUCCI [Opens in a new window]
NICOLA CAVALLUCCI*
Affiliation:
Mathematisches Institut, Universitat Köln, Weyertal 86–90, 50931 Köln, Germany
*
e-mail: [email protected]
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Abstract

We show continuity under equivariant Gromov–Hausdorff convergence of the critical exponent of discrete, non-elementary, torsion-free, quasiconvex-cocompact groups with uniformly bounded codiameter acting on uniformly Gromov-hyperbolic metric spaces.

Keywords

Gromov hyperbolicityGromov–Hausdorff convergenceentropycontinuityconvex-cocompact

MSC classification

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 4 , April 2023 , pp. 1189 - 1221
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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