Questions tagged [gromov-boundary]
Apt for questions on the Gromov boundary which is the set of all points at infinity. For instance, the Gromov boundary of the real line is two points, corresponding to positive and negative infinity.
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Gromov Boundary of metric space with finite diameter
$\textbf{Definition:}$
Let $X$ be a quasi-geodesic metric space. The Gromov boundary $\partial X := \{ \gamma : [0, \infty) \to X \mid \gamma \text{ is a quasi-geodesic ray} \} / {\sim}$
where quasi-...
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How to understand the compactification of the upper half plane as motivation for Gromov compactification of an arbitrary $\delta$-hyperbolic space??
Let $X$ be a $\delta$-hyperbolic space. Let us define an equivalence relation on geodesic rays $\gamma_1, \gamma_2 :[0,\infty) \rightarrow X$ by {$\gamma_1 \sim \gamma_2\,\, \iff d(\gamma_1(t),\...