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arXiv · 2501.05876

On the approaching geodesics property

Leandro Arosio·Matteo Fiacchi
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Abstract

We survey some recent results and open questions on the approaching geodesics property and its application to the study of the Gromov and horofunction compactifications of a proper geodesic Gromov metric space. We obtain results on the dynamics of isometries and we exhibit an example of a Gromov hyperbolic domain of $\mathbb{C}$ which does not satisfy the approaching geodesic property.

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Leandro Arosio, Matteo Fiacchi. 2025-01-10. On the approaching geodesics property. https://doi.org/10.1007/s40574-024-00442-7

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