# Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups

@inproceedings{Besson2021FinitenessTF, title={Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups}, author={G'erard Besson and Gilles Courtois and Sylvestre Gallot and Andrea Sambusetti}, year={2021} }

In this article we prove that the set of torsion-free groups acting by isometries on a hyperbolic metric space whose entropy is bounded above and with a compact quotient is finite. The number of such groups can be estimated in terms of the hyperbolicity constant and of an upper bound of the entropy of the space and of an upper bound of the diameter of its quotient. As a consequence we show that the set of non cyclic torsion-free δ-hyperbolic marked groups whose entropy is bounded above by a… Expand

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