Results 11 to 20 of about 353 (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 hyperbolicity of planar graphs [PDF]
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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Worm Domains are not Gromov Hyperbolic. [PDF]
J Geom Anal, 2023 AbstractWe show that Worm domains are not Gromov hyperbolic with respect to the Kobayashi distance.
Arosio L, Dall'Ara GM, Fiacchi M.
europepmc +7 more sources
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.
Hästö, Peter +3 more
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Detours and Gromov hyperbolicity [PDF]
, 2008 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].
Buckley, Stephen M. +1 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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Stability of Gromov hyperbolicity [PDF]
, 2009 A main problem when studying any mathematical property is to determine its stability, i.e., under what type of perturbations it is preserved. With this aim, here we study the stability of Gromov hyperbolicity, a property which has been proved to be fruitful in many fields.
Portilla, Ana +2 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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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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