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On the tree-likeness of hyperbolic spaces

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arxiv 1105.3925 v1 pith:HCB7BGOQ submitted 2011-05-19 math.MG

Matthias Hamann This is my paper · ORCID
classification math.MG
keywords boundaryhyperbolictreesmathbbspacespacesassouadbounded
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abstract

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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  1. Characterizing Hyperbolicity in Graphs

    math.MG 2026-07 reject novelty 6.0 of 10

    The paper claims an exact formula for the maximal Gromov delta among quadruples of fixed diameter in the hyperbolic plane and uses it to derive a normalized graph hyperbolicity score.

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