منابع مشابه
Detours and Gromov hyperbolicity
The notion of Gromov hyperbolicity was introduced by Gromov in the setting of geometric group theory [G1], [G2], but has played an increasing role in analysis on general metric spaces [BHK], [BS], [BBo], [BBu], and extendability of Lipschitz mappings [L]. In this theory, it is often additionally assumed that the hyperbolic metric space is proper and geodesic (meaning that closed balls are compa...
متن کاملGromov Hyperbolicity in Mycielskian Graphs
Since the characterization of Gromov hyperbolic graphs seems a too ambitious task, there are many papers studying the hyperbolicity of several classes of graphs. In this paper, it is proven that every Mycielskian graph GM is hyperbolic and that δ(GM) is comparable to diam(GM). Furthermore, we study the extremal problems of finding the smallest and largest hyperbolicity constants of such graphs;...
متن کاملGromov Hyperbolicity in Strong Product Graphs
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity const...
متن کاملGromov hyperbolicity and the Kobayashi metric
It is well known that the unit ball endowed with the Kobayashi metric is isometric to complex hyperbolic space and in particular is an example of a negatively curved Riemannian manifold. One would then suspect that when Ω ⊂Cd is a domain close to the unit ball then (Ω ,KΩ ) should be negatively curved (in some sense). Unfortunately, for general domains the Kobayashi metric is no longer Riemanni...
متن کاملGromov Hyperbolicity of Certain Conformal Invariant Metrics
The unit ball B is shown to be Gromov hyperbolic with respect to the Ferrand metric λBn and the modulus metric μBn , and dimension dependent upper bounds for the Gromov delta are obtained. In the two-dimensional case Gromov hyperbolicity is proved for all simply connected domains G. For λG also the case G = R n \ {0} is studied.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2008
ISSN: 0019-2082
DOI: 10.1215/ijm/1258554351