Gromov hyperbolic spaces

By Jussi Väisälä. 2005

224 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/380def3ec24a700ac451e9121caece775255ad74

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

High-Dimensional Menger-Type Curvatures—Part II: d-Separation and a Menagerie of Curvatures (2008, background): “The Gromov product is indeed a natural quantity for this purpose since it is quasi-isometric to distances to “geodesic curves” in any fixed ball [28].”
Uniformization of Sierpiński carpets in the plane (2010, background): “This action is uniformly quasi-Mobius, i.e., there exists a homeomorphism η :[ 0, ∞] → [0, ∞] such that each g ∈ G acts as anη-quasi-Mobius map on ∂∞G (this goes back to the remark preceding [24, Theorem 5.4]; it easily follows from [ 35, Theorem 5.38 ]).”
Chordality and hyperbolicity of a graph (2009, result): “We also refer to [2, 13, 16, 93] for some equivalent and very accessible definitions of Gromov hyperbolicity which involve some other comparable parameters.”
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “ncept is not to be confused with the more common notion of a pseudometric, which satises (I), (III), and (IV), but not necessarily (II). The term \metametric" was introduced by J. Vaisala in [87]. If Dis a metametric, we dene its domain of re exivity as the set Z refl := fx2Z : D(x;x) = 0g. Obv”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, background): “One of many alternative definitions for Gromov-hyperbolic spaces is as follows (background material on this topic can be found in the monographs [23, 8, 24, 64]).”