Results 31 to 40 of about 462 (153)

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, D, Nowak, PW
openaire   +3 more sources

Gromov hyperbolic graphs

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, José M. Rodríguez, Sergio Bermudo, José M. Sigarreta   +3 more
openaire   +2 more sources

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
openaire   +4 more sources

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, Moreno Casablanca, Rocío, Cruz, Amauris de la, Rodríguez, José M.   +3 more
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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, Ana Portilla, José M. Rodríguez, Eva Tourís   +3 more
openaire   +2 more sources

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity [PDF]

Journal of Mathematical Analysis and Applications
We 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
openalex   +3 more sources

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, Shanmugalingam, Nageswari, Xie, Xiangdong   +2 more
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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, Granados, Ana, Pestana, Domingo, Rodríguez, José M.   +3 more
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Curvature‐dimension condition of sub‐Riemannian α$\alpha$‐Grushin half‐spaces

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We provide new examples of sub‐Riemannian manifolds with boundary equipped with a smooth measure that satisfy the RCD(K,N)$\mathsf {RCD}(K, N)$ condition. They are constructed by equipping the half‐plane, the hemisphere and the hyperbolic half‐plane with a two‐dimensional almost‐Riemannian structure and a measure that vanishes on their ...
Samuël Borza, Kenshiro Tashiro
wiley   +1 more source

Dual spaces of geodesic currents

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract Every geodesic current on a hyperbolic surface has an associated dual space. If the current is a lamination, this dual embeds isometrically into a real tree. We show that, in general, the dual space is a Gromov hyperbolic metric tree‐graded space, and express its Gromov hyperbolicity constant in terms of the geodesic current.
Luca De Rosa, Dídac Martínez‐Granado
wiley   +1 more source