Results 11 to 20 of about 17,964 (136)
Gromov hyperbolicity and quasihyperbolic geodesics [PDF]
Annales scientifiques de l'École normale supérieure, 2014 We characterize Gromov hyperbolicity of the quasihyperbolic metric space (Ω,k) by geometric properties of the Ahlfors regular length metric measure space (Ω,d,μ). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.
Lammi, Päivi +3 more
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Gromov hyperbolic cubic graphs [PDF]
Open Mathematics, 2012 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 ...
Pestana Domingo +3 more
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Knot graphs and Gromov hyperbolicity [PDF]
Mathematische Zeitschrift, 2022 We define a broad class of graphs that generalize the Gordian graph of knots. These knot graphs take into account unknotting operations, the concordance relation, and equivalence relations generated by knot invariants. We prove that overwhelmingly, the knot graphs are not Gromov hyperbolic, with the exception of a particular family of quotient knot ...
Stanislav Jabuka +2 more
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Hyperbolicity vs. Amenability for Planar Graphs. [PDF]
Discrete Comput Geom, 2017 The aim of this paper is to clarify the relationship between Gromov-hyperbolicity and amenability for planar ...
Federici B, Georgakopoulos A.
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Gromov hyperbolicity of planar graphs
Open Mathematics, 2013 AbstractWe prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this ...
Cantón Alicia +3 more
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Bounds on Gromov hyperbolicity constant [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2015 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 $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ 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 ...
Hernández, Verónica +2 more
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Embeddings of Gromov Hyperbolic Spaces [PDF]
Geometric And Functional Analysis, 2000 To state the main result of the paper we start with two definitions: A metric space \(X\) has ``bounded growth at some scale'' if there are constants \(R>r>0\) and a positive integer \(N\) such that every open ball of radius \(R\) in \(X\) can be covered by \(N\) open balls of radius \(r\). A metric space \(X\) is ``roughly similar'' to a metric space \
Bonk, M., Schramm, O.
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A new characterization of Gromov hyperbolicity for negatively curved surfaces [PDF]
, 2006 In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or, Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a
Tourís, E. +5 more
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Discrete Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergio Bermudo +3 more
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The role of funnels and punctures in the Gromov hyperbolicity of Riemann surfaces [PDF]
, 2006 27 pages, no figures.-- MSC2000 codes: 30F20, 30F45.MR#: MR2243795 (2007e:30063)Zbl#: Zbl 1108.30031We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense.
Tourís, Eva +2 more
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