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arXiv · 1606.01575

Properties of sets of isometries of Gromov hyperbolic spaces

Eduardo Oregón-Reyes
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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 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.

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Eduardo Oregón-Reyes. 2016-06-05. Properties of sets of isometries of Gromov hyperbolic spaces. https://arxiv.org/abs/1606.01575

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