Boundaries of hyperbolic groups
By Ilya Kapovich, Nadia Benakli. 2002
273 citations recorded by the source corpus.
In this paper we survey the known results about boundaries of word-hyperbolic groups.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/abca2e9a6815b8f2b1124dc2c2599b1570bf445e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Bruce Kleiner
- S. Keith
- H. Oh
- Greg Hjorth
- Oded Schramm
- Russell Lyons
- Alexander S. Kechris
- Minju M. Lee
In Geometry and Topology
- Greg Hjorth
- Bruce Kleiner
- Russell Lyons
- Alexander S. Kechris
- S. Keith
- Minju M. Lee
- H. Oh
- Itai Benjamini
In Mathematical Physics
- Russell Lyons
- Alexander S. Kechris
- Itai Benjamini
- Oded Schramm
- Greg Hjorth
- Minju M. Lee
- Bruce Kleiner
- H. Oh
Citations in the corpus
- Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization (2003, unknown): “See the recent survey [7] for a general discussion of boundaries of Gromov hyperbolic spaces.”
- Modulus and the Poincaré inequality on metric measure spaces (2003, methodology): “This latter result is of particular interest for non-smooth uniformization procedures in connection with Thurston’s Hyperbolization Conjecture (see [ KB02 , pp.24-26]).”
- The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity (2006, background): “In this section we review some facts about Gromov hyperbolicity, see [31], [30], [16], [34], [41].”
- Unimodular random trees (2012, background): “See the survey [19] for information on the boundary of a word-hyperbolic group.”
- Invariant Measures for Horospherical Actions and Anosov Groups (2020, background): “Let us recall some basic terminologies for hyperbolic groups for which we refer to [7] and [18].”
- Random walks on co-compact fuchsian groups (2013, unknown): “Our results also yield explicit rates for the convergence (3), and imply that the Martin kernel Kr(x, ζ) is Hölder continuous in ζ relative to the usual Euclidean metric (or any visual metric — see [23] for the definition) on S1 = ∂Γ.”
- Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations (2005, methodology): “For the definition and basic properties of hyperbolic groups, we refer the reader to [Gr], [GdlH], [CPD], [KB].”