Rigidity of quasi-isometries for some hyperbolic buildings

By M. Bourdon, H. Pajot. 2000

103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7f4236fc8291308eb7e13a29c7520dd691b1b961

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The Geometry and Topology of Coxeter Groups (2025, background): “Fuchsian buildings, as well as, other buildings associated to hyperbolic reflection groups are discussed in [30, 31, 32, 111, 133, 245].”
Harmonic analysis, cohomology, and the large-scale geometry of amenable groups (2004, background): “the survey [21]; see also [26] and [13]), more attention has been paid recently to "smaller" (e.”
Quasisymmetric parametrizations of two-dimensional metric spheres (2001, background): “[19, 4 ]), which mediates between the quasisymmetric distortion and the “conformal” distortion, and a modulus comparison proposition which allows one to relate (under suitable conditions) the 2-modulus of a pair of continua E, F ⊂ Z with the combinatorial 2-modulus of their discrete approximations ”
Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “The Gromov boundaries of certain hyperbolic buildings Ipq, introduced by Bourdon [10], [11], and later studied by Bourdon and Pajot [12], [13], provide another source of metric measure spaces with good firstorder analytic properties.”
The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity (2006, background): “that every quasi-isometry of X lies at finite distance from a unique isometry [51], [44], [12].”
Harmonicity of Quasiconformal Measures and Poisson Boundaries of Hyperbolic Spaces (2004, methodology): “Throughout this example we refer to [ BP00 ] for details and proofs of stated facts.”
Factor and normal subgroup theorems for lattices in products of groups (2006, methodology): “[ BP00 ]) is an open subgroup which is non-compact and of infinite index.”
Geometry and rigidity of mapping class groups (2008, background): “Groups quasi-isometric to Fuchsian buildings (see Bourdon and Pajot [9] and Xie [59]).”
Combinatorial modulus, the Combinatorial Loewner Property, and Coxeter groups (2010, unknown): “Indeed in this case ∂Γ possesses a self-similar metric δ such that (∂Γ, δ) is an Loewner space [BP00].”
Quasi-actions on trees I. Bounded valence (2000, unknown): “[ BP00 ], [FM99], [FM00], [FM02], [KL97a], [KL97b], [Tab00]; see [Far97] for a survey.”