Results 31 to 40 of about 353 (136)
Computing the Gromov hyperbolicity of a discrete metric space
, 2015 We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,
Vigneron, Antoine E. +6 more
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A characterization of Gromov hyperbolicity of surfaces with variable negative curvature [PDF]
, 2009 In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature K≤ -k² < 0, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is,
Tourís, Eva +3 more
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Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics
The Journal of Geometric Analysis, 2022 We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a cone arc. This result provides a new approach to the elementary metric geometry question, formulated in \cite[Question 2]{Hei89}, which has been studied by Gehring, Hag, Martio and Heinonen. As an application, we obtain a
Qingshan Zhou, Yaxiang Li, Antti Rasila
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A new characterization of Gromov hyperbolicity for negatively curved surfaces
, 2021 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., Rodríguez, J. M.
core
Computing the Gromov hyperbolicity constant of a discrete metric space
, 2012 Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields.
Ismail, Anas
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Uniform growth in small cancellation groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract An open question asks whether every group acting acylindrically on a hyperbolic space has uniform exponential growth. We prove that the class of groups of uniform uniform exponential growth acting acylindrically on a hyperbolic space is closed under taking certain geometric small cancellation quotients.
Xabier Legaspi, Markus Steenbock
wiley +1 more source
Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
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Gromov hyperbolic groups and the Macaev norm [PDF]
Pacific Journal of Mathematics, 2006 Let \(\Gamma\) be a Gromov hyperbolic group with a finite set \(A\) of generators. One can consider three quantities: the Coornaert-Papadopoulos topological entropy \(h_{top}(\Sigma(\infty))\) of the subshift associated to \((\Gamma,A)\), Voiculescu's invariant \(k^-_\infty(\lambda_A)\), and the growth entropy \(\text{gr}(\Gamma,A)\). The author proves
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Circle packings, renormalizations, and subdivision rules
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we use iterations of skinning maps on Teichmüller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certain subdivision rules. We characterize when the skinning map has bounded image.
Yusheng Luo, Yongquan Zhang
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Graph potentials and topological quantum field theories
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans +2 more
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