JournalsggdVol. 12, No. 3pp. 889–910

Properties of sets of isometries of Gromov hyperbolic spaces

  • Eduardo Oregón-Reyes

    Pontificia Universidad Católica de Chile, Santiago, Chile
Properties of sets of isometries of Gromov hyperbolic spaces cover
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Abstract

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 of2×22 \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.

Cite this article

Eduardo Oregón-Reyes, Properties of sets of isometries of Gromov hyperbolic spaces. Groups Geom. Dyn. 12 (2018), no. 3, pp. 889–910

DOI 10.4171/GGD/468