Results 21 to 30 of about 149 (127)

The horofunction boundary of a Gromov hyperbolic space

Mathematische Annalen, 2022
We highlight a condition, the approaching geodesics property, on a proper geodesic Gromov hyperbolic metric space, which implies that the horofunction compactification is topologically equivalent to the Gromov compactification. It is known that this equivalence does not hold in general. We prove using rescaling techniques that the approaching geodesics
Arosio, L, Fiacchi, M, Gontard, S, Guerini, L   +3 more
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Hyperbolic Metric Spaces and Stochastic Embeddings

Forum of Mathematics, Sigma
Stochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science.
Chris Gartland
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Rough isometry between Gromov hyperbolic spaces and uniformization

Annales Fennici Mathematici, 2021
17 ...
Lindquist, Jeff, Shanmugalingam, Nageswari   +1 more
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Boundary rigidity of Gromov hyperbolic spaces

Geometriae Dedicata
We introduce the concept of boundary rigidity for Gromov hyperbolic spaces. We show that a proper geodesic Gromov hyperbolic space with a pole is boundary rigid if and only if its Gromov boundary is uniformly perfect. As an application, we show that for a non-compact Gromov hyperbolic complete Riemannian manifold or a Gromov hyperbolic uniform graph ...
Liang, Hao, Zhou, Qingshan
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Recent results on hyperbolicity on unitary operators on graphs [PDF]

Discrete Mathematics Letters, 2023
Jesús A. Méndez, Rosalio Reyes, Jose M. Rodríguez, José M. Sigarreta   +3 more
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Quasi-geodesic segments and Gromov hyperbolic spaces [PDF]

Geometriae Dedicata, 1996
Let \(X\) be a geodesic metric space. The author makes the following definitions: For \(\lambda\geq 1\), a path \(\varphi: [a,b]\to X\) is said to be a \(\lambda\)-chord-arc curve if for every \([c,d] \subset[a,b]\), we have \[ \text{length} \varphi \bigl([c,d]\bigr) \leq \lambda \bigl|\varphi (c)- \varphi(d) \bigr|.
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Number of least area planes in Gromov hyperbolic $3$-spaces [PDF]

Proceedings of the American Mathematical Society, 2010
We show that for a generic simple closed curve C in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exist a unique least area plane P in X with asymptotic boundary C. This result has interesting topological applications for constructions of canonical 2-dimensional objects in 3-manifolds.
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Marked length spectra of Gromov hyperbolic space

, 2023
We change the statement of the early version for ...
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Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups

, 2021
In this article we prove that the set of torsion-free groups acting by isometries on a hyperbolic metric space whose entropy is bounded above and with a compact quotient is finite. The number of such groups can be estimated in terms of the hyperbolicity constant and of an upper bound of the entropy of the space and of an upper bound of the diameter of ...
Besson, Gérard, Courtois, Gilles, Gallot, Sylvestre, Sambusetti, Andrea   +3 more
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Properties of sets of isometries of Gromov hyperbolic spaces [PDF]

Groups, Geometry, and Dynamics, 2018
We prove an inequality concerning isometries of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral radius, and shows that sets of isometries behave like sets of 2 ...
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