منابع مشابه
Gromov Hyperbolicity of Denjoy Domains with Hyperbolic and Quasihyperbolic Metrics
We obtain explicit and simple conditions which in many cases allow one decide, whether or not a Denjoy domain endowed with the Poincaré or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows to deduce the non-hyperbolicity of any periodic Denjoy domain.
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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...
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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 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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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...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2006
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-006-9102-z