Results 11 to 20 of about 149 (127)
The hyperbolicity constant of infinite circulant graphs
Open Mathematics, 2017 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.
Rodríguez José M., Sigarreta José M.
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Mathematical Properties of the Hyperbolicity of Circulant Networks
Advances in Mathematical Physics, 2015 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.
Juan C. Hernández +2 more
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Gromov Hyperbolicity, Teichm\"{u}ller Space \& Bers Boundary
Journal of Mathematics Research, 2013 We present in this paper a new proof of a theorem by Wolf-Masur stipulating that Teichmüller space of surface with genus g ≥ 2 equipped with the Teichmüller metric is not hyperbolic in the sense of Gromov, by constructing a family of points that converge to the Bers boundary contradicting a property proved by Bers in 1983.To our knowledge, there are ...
Abdelhadi Belkhirat, Khaled Batainah
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Flats in Spaces with Convex Geodesic Bicombings
Analysis and Geometry in Metric Spaces, 2016 In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments
Descombes Dominic, Lang Urs
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Teichmuller Space is Not Gromov Hyperbolic
, 1994 We prove that the Teichmuller Space of Riemann Surfaces of genus g>1, equipped with the Teichmuller metric, is not a Gromov Hyperbolic space.
Masur, Howard A., Wolf, Michael
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Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces
Analysis and Geometry in Metric Spaces, 2016 Let (Z, d, μ) be a compact, connected, Ahlfors Q-regular metric space with Q > 1. Using a hyperbolic filling of Z,we define the notions of the p-capacity between certain subsets of Z and of theweak covering p-capacity of path families Γ in Z.We show ...
Lindquist Jeff
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Expositiones Mathematicae, 2005 This is a mini monograph on Gromov hyperbolic spaces, which are not necessarily geodesic or proper. As the author notes, the purpose of the article is to give a fairly detailed treatment of the basic theory of hyperbolic spaces more general than proper and geodesic.
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Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces [PDF]
Duke Mathematical Journal, 2006 A metric space $X$ has {\em Markov type} 2, if for any reversible finite-state Markov chain $\{Z_t\}$ (with $Z_0$ chosen according to the stationary distribution) and any map $f$ from the state space to $X$, the distance $D_t$ from $f(Z_0)$ to $f(Z_t)$ satisfies $\E(D_t^2) \le K^2 t \E(D_1^2)$ for some $K=K(X)2$) has Markov type 2; this proves a ...
Naor, Assaf +3 more
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Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
Forum of Mathematics, SigmaWe prove that, for any countable acylindrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph $\Gamma (G,S)$ is hyperbolic, $|\partial \Gamma (G,S)|>2$ , the natural action of G on ...
Koichi Oyakawa
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Non-amenability and visual Gromov hyperbolic spaces [PDF]
Groups, Geometry, and Dynamics, 2017 We prove that a uniformly coarsely proper hyperbolic cone over a bounded metric space consisting of a finite union of uniformly coarsely connected components each containing at least two points is non-amenable and apply this to visual Gromov hyperbolic spaces.
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