Rigidity for Quasi-Möbius Group Actions
By M. Bonk, Bruce Kleiner. 2000
112 citations recorded by the source corpus.
If a group acts by uniformly quasi-Mobius homeomorphisms on a compact Ahlfors n-regular space of topological dimension n such that the induced action on the space of distinct triples is cocompact, then the action is quasisymmetrically conjugate to an action on the standard n-sphere by Mobius transformations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c670b32458a5a900ea44ab283749214ffc859fb7
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In Geometry and Topology
- S. Merenkov
- M. Bonk
- Bruce Kleiner
- Stephen M. Buckley
- G. Besson
- Kai Rajala
- M. Bourdon
- Matias Carrasco Piaggio
In Mathematical Physics
- S. Merenkov
- M. Bonk
- Bruce Kleiner
- Terence Tao
- Kai Rajala
- Yehuda Shalom
- Reto Müller
- Michael Kapovich
Citations in the corpus
- Rigidity of amalgamated product in negative curvature (2005, background): “Now the cocompact group Γ acts uniformly quasi-conformally on (∂X̃, d), ([4] and [19] Theorem 5.”
- Quasisymmetric rigidity of square Sierpinski carpets (2011, methodology): “angent spaces can be dened as Gromov-Hausdor limits of pointed metric spaces obtained by rescaling the underlying metric (see [BBI, Chapters 7,8] and [DS, Chapter 8] for the general definitions, and [BK2] for applications very similar in spirit to the present paper). As we will need this only for th”
- Quasisymmetric parametrizations of two-dimensional metric spheres (2001, background): “However, if an n-regular n-sphere admits an appropriately large group of symmetries, then it must be quasisymmetrically homeomorphic to the standard n-sphere, see [ 2 ].”
- Harmonic measures versus quasiconformal measures for hyperbolic groups (2008, unknown): “For example, M. Bonk and B. Kleiner proved that a group admits a cocompact Kleinian action on the hyperbolic space H n , n ≥ 3, if and only if its boundary has topological dimension n − 1 and carries an Ahlfors-regular metric of dimension n − 1 [8].”
- Metric space inversions, quasihyperbolic distance, and uniform spaces (2008, background): “3.B. Sphericalization. As mentioned already, our denition of Invp(X) mimics a construction of Bonk and Kleiner [ BK02 , Lemma 2.2, p.87].”