منابع مشابه
Strong Hyperbolicity
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(−1) spaces are strongly hyperbolic. On the way, we determine the best ...
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...
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We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn’s Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Combination Theorem. AMS subject classification = 20F32(Primary), 57M50(Secondary)
متن کاملHausdorr Dimension, Strong Hyperbolicity and Complex Dynamics
x0. Introduction Let X be a compact metric space and assume that f : X ! X is a continuous map. Denote by the nonwandering set of f. An interesting and a nontrivial invariant of f is HD(()-the Hausdorr dimension of. It is usually a highly nontrivial problem to nd HD((). The seminal work of Bowen Bow2] gives HD(() as the solution to P(tt) = 0 for some special expanding maps. Here P(g) denotes th...
متن کاملHausdorr Dimension, Strong Hyperbolicity and Complex Dynamics X0. Introduction
Let X be a compact metric space and assume that f : X ! X is a continuous map. Denote by the nonwandering set of f. An interesting and a nontrivial invariant of f is HD(()-the Hausdorr dimension of. It is usually a highly nontrivial problem to nd HD((). The seminal work of Bowen Bow2] gives HD(() as the solution to P(tt) = 0 for some special expanding maps. Here P(g) denotes the topological pre...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2016
ISSN: 1661-7207
DOI: 10.4171/ggd/372