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 real matrices. Among the consequences of the inequality, we obtain the continuity of the joint stable length and an analogue of Berger–Wang theorem.
Cite this article
Eduardo Oregón-Reyes, Properties of sets of isometries of Gromov hyperbolic spaces. Groups Geom. Dyn. 12 (2018), no. 3, pp. 889–910DOI 10.4171/GGD/468