On the tree-likeness of hyperbolic spaces

Details On the tree-likeness of hyperbolic spaces On the tree-likeness of hyperbolic spaces

2011-05-19

arxiv.org/abs/1105.3925v1

Mathematics

Metric Geometry

20 pages

Scientific paper

In proper hyperbolic geodetic spaces we construct rooted $\mathbb R$-trees with the following properties. On the one hand, every ray starting at the root is quasi-geodetic; so these $\mathbb R$-trees represent the space itself well. At the same time, the trees boundary reflects the boundary of the space in that the number of disjoint rays to a boundary point is bounded in terms of the (Assouad) dimension of the hyperbolic boundary.

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