Otal-Peign\'e's Theorem for Gromov-hyperbolic spaces

Nicola Cavallucci

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arXiv · 2412.10801

Otal-Peign\'e's Theorem for Gromov-hyperbolic spaces

Nicola Cavallucci

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Abstract

We extend the classical Otal-Peign\'e's Theorem to the class of proper, Gromov-hyperbolic spaces that are line-convex. Namely, we prove that when a group acts discretely and virtually freely by isometries on a metric space in this class then its critical exponent equals the topological entropy of the geodesic flow of the quotient metric space. We also show examples of proper, Gromov-hyperbolic spaces that are not line-convex and for which the statement fails.

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Nicola Cavallucci. 2024-12-14. Otal-Peign\'e's Theorem for Gromov-hyperbolic spaces. https://arxiv.org/abs/2412.10801

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