On the approaching geodesics property

Published 10 Jan 2025 in math.CV and math.MG | (2501.05876v1)

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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