Results 31 to 40 of about 435 (132)
Discrete Mathematics, 2013 Abstract In this paper we prove that the study of the hyperbolicity on graphs can be reduced to the study of the hyperbolicity on simpler graphs. In particular, we prove that the study of the hyperbolicity on a graph with loops and multiple edges can be reduced to the study of the hyperbolicity in the same graph without its loops and multiple edges ...
Jean-Marie Vilaire +3 more
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Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity [PDF]
Journal of Mathematical Analysis and ApplicationsWe study in the setting of a metric space $\left( X,d\right) $ some generalizations of four hyperbolic-type metrics defined on open sets $G$ with nonempty boundary in the $n-$dimensional Euclidean space, namely Gehring-Osgood metric, Dovgoshey- Hariri-Vuorinen metric, Nikolov-Andreev metric and Ibragimov metric.
Marcelina Mocanu
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Gromov Hyperbolicity in Strong Product Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 If X is a geodesic metric space and $x_1,x_2,x_3\in X$, a geodesic triangle $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-hyperbolic $($in the Gromov sense$)$ if any side of $T$ is contained in a $\delta$-neighborhood of the union of the two other sides, for every ...
Carballosa, Walter +3 more
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Average Gromov hyperbolicity and the Parisi ansatz
Advances in Mathematics, 2021 Gromov hyperbolicity of a metric space measures the distance of the space from a perfect tree-like structure. The measure has a "worst-case" aspect to it, in the sense that it detects a region in the space which sees the maximum deviation from tree-like structure.
Sourav Chatterjee, Leila Sloman
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Gromov hyperbolicity of periodic planar graphs [PDF]
Acta Mathematica Sinica, English Series, 2013 The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.
Canton Pire, Alicia +3 more
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The topology of balls and Gromov hyperbolicity of Riemann surfaces [PDF]
Differential Geometry and its Applications, 2004 Research by first two authors (A.P. and J.M.R.) was partially supported by a grant from DGI (BFM 2000-0022), Spain. Research by third author (E.T.)was supported by a grant from DGI (BFM 2000-0022), Spain.
Ana Portilla +2 more
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Uniformity from Gromov hyperbolicity
Illinois Journal of Mathematics, 2008 We show that in a metric space $X$ with annular convexity, uniform domains are precisely those Gromov hyperbolic domains whose quasiconformal structure on the Gromov boundary agrees with that on the boundary in $X$. As an application, we show that quasimobius maps between geodesic spaces with annular convexity preserve uniform domains.
Herron, David +2 more
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Coboundary expansion and Gromov hyperbolicity
, 2023 We prove that if a compact $n$-manifold admits a sequence of residual covers that form a coboundary expander in dimension $n-2$, then the manifold has Gromov-hyperbolic fundamental group. In particular, residual sequences of covers of non-hyperbolic compact connected irreducible 3-manifolds are not 1-coboundary expanders.
Kielak, Dawid, Nowak, Piotr W.
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Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics [PDF]
Complex Variables and Elliptic Equations, 2009 In this article, we investigate the Gromov hyperbolicity of Denjoy domains equipped with the hyperbolic or the quasihyperbolic metric. The focus are on comparative or decomposition results, which allow us to reduce the question of whether a given domain is Gromov hyperbolic to a series of questions concerning simpler domains.
Peter Hästö +3 more
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Thurston obstructions and tropical geometry
Bulletin of the London Mathematical Society, EarlyView.Abstract We describe an application of tropical moduli spaces to complex dynamics. A post‐critically finite branched covering φ$\varphi$ of S2$S^2$ induces a pullback map on the Teichmüller space of complex structures of S2$S^2$; this descends to an algebraic correspondence on the moduli space of point‐configurations of P1$\mathbb {P}^1$.
Rohini Ramadas
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