# Questions tagged [gromov-hyperbolic-spaces]

Gromov hyperbolic spaces, also known as $\delta$-hyperbolic spaces, are geodesic spaces in which every triangle is thin. Hyperbolic groups are fundamental examples of Gromov hyperbolic spaces in geometric group theory.

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### Hyperbolic metric spaces 2

I am trying to prove a lemma in Burago's "A Course in Metric Spaces" (Exercise 8.4.4, p.286). Here is a link to a different person's question about the very next exercise in that book, which also ...
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### Topology on the Gromov Boundary of a Hyperbolic Space

Let $X$ be a proper geodesic metric space that is $\delta$-hyperbolic. Definition. We define the Gromov boundary $\partial X$ of $X$ as the set of all the geodesic rays $c:[0, \infty)\to X$, where ...
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### Gromov hyperbolic Space example

I'm reading the original paper of Gromov Hyperbolic Groups. There, he gives the next example Let $X_0,d$ be an arbitrary metric space ande let $f\colon\mathbb{R}\rightarrow \mathbb{R}$ be a positive ...
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### Hyperbolic groups from Dehn functions

Hyperbolic groups may be defined as finitely generated groups admitting a linear Dehn function. I wonder whether it is possible to prove most of the classifical properties of hyperbolic groups in this ...
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### Deck transformations and Gromov Hyperbolicity

I would like to ask, once more, for some references in Gromov-hyperbolic spaces. The question is specifically the following: Does someone know any alternative reference, alternative proof, anything, ...
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### References for Hyperbolic Graph Theory

I'm sorry to disturb you but I really got stuck! I can't find any clear and, somewhat, complete reference for this topic. I'm looking for a book, or review, or survey or course notes regarding "...