Results 51 to 60 of about 17,194 (132)

A Gromov Hyperbolic metric and Möbius transformations

, 2020
We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit ball or in the upper half space, and prove sharp comparison inequalities between the Gromov hyperbolic metric and some hyperbolic type metrics. We also obtain several sharp distortion inequalities for the Gromov hyperbolic metric under some families of Möbius transformations.
Xu, Xiaoxue, Wang, Gendi, Zhang, Xiaohui
openaire   +2 more sources

Exactness and the topology of the space of invariant random equivalence relations

Proceedings of the London Mathematical Society, Volume 132, Issue 5, May 2026.
Abstract We characterize exactness of a countable group Γ$\Gamma$ in terms of invariant random equivalence relations (IREs) on Γ$\Gamma$. Specifically, we show that Γ$\Gamma$ is exact if and only if every weak limit of finite IREs is an amenable IRE.
Héctor Jardón‐Sánchez, Sam Mellick, Antoine Poulin, Konrad Wróbel   +3 more
wiley   +1 more source

Non‐amenability of mapping class groups of infinite‐type surfaces and graphs

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract This paper completely determines the non‐amenability of the mapping class groups of infinite‐type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non‐amenable stabiliser of a point at infinity of a coarsely bounded generated hyperbolic Polish group, and exhibits a class of mapping class
Yusen Long
wiley   +1 more source

Gromov hyperbolic spaces

Expositiones Mathematicae, 2005
This is a mini monograph on Gromov hyperbolic spaces, which are not necessarily geodesic or proper. As the author notes, the purpose of the article is to give a fairly detailed treatment of the basic theory of hyperbolic spaces more general than proper and geodesic.
openaire   +1 more source

Graphical small cancellation and hyperfiniteness of boundary actions

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned‐off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented) classical small cancellation groups, admit hyperfinite boundary actions, more precisely, the orbit equivalence ...
Chris Karpinski, Damian Osajda, Koichi Oyakawa   +2 more
wiley   +1 more source

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
wiley   +1 more source

Geometric characterizations of Gromov hyperbolicity [PDF]

, 2018
We prove the equivalence of three different geometric properties of metric-measure spaces with controlled geometry. The first property is the Gromov hyperbolicity of the quasihyperbolic metric.
Balogh, Zoltán M., Buckley, Stephen M.
core  

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
wiley   +1 more source

Uniformization of Intrinsic Gromov Hyperbolic Spaces

Computational Methods and Function Theory
The purpose of this paper is to provide a uniformization procedure for Gromov hyperbolic spaces, which need not be geodesic or proper. We prove that the conformal deformation of a Gromov hyperbolic space is a bounded uniform space. Further, we show that there is a natural quasi-isometry between the Gromov boundary and the metric boundary of the ...
Allu, Vasudevarao, Jose, Alan P
openaire   +2 more sources