Groups, Geometry, and Dynamics


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Volume 12, Issue 3, 2018, pp. 889–910
DOI: 10.4171/GGD/468

Published online: 2018-08-13

Properties of sets of isometries of Gromov hyperbolic spaces

Eduardo Oregón-Reyes[1]

(1) Pontificia Universidad Católica de Chile, Santiago, Chile

We prove an inequality concerning isometries of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral radius, and shows that sets of isometries behave like sets of$2 \times 2$ real matrices. Among the consequences of the inequality, we obtain the continuity of the joint stable length and an analogue of Berger–Wang theorem.

Keywords: Gromov hyperbolic space, stable length, joint spectral radius

Oregón-Reyes Eduardo: Properties of sets of isometries of Gromov hyperbolic spaces. Groups Geom. Dyn. 12 (2018), 889-910. doi: 10.4171/GGD/468