1996/08/01 by Frédéric Paulin · 99 citations
Mathematics · #Bijection, injection and surjection #Boundary (topology) #Combinatorics #Computer science #Construct (python library) #Data mining #Geometric and Algebraic Topology #Group (periodic table) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Mathematics and Applications #Measure (data warehouse) #Physics #Pure mathematics
paper · doi:10.1112/jlms/54.1.50
published in Journal of the London Mathematical Society 54(1), 50-74 (Wiley)
openalex publication_date 1996/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We construct on the boundary of a hyperbolic group (in Gromov's sense) a natural visual measure and a natural crossratio. We prove that the I-quasiconformal homeomorphisms (in Pansu's sense) between the boundaries of hyperbolic groups are the quasimöbius maps (that is, the bijections that almost preserve the crossratios), and that they are the extensions of the quasi-isometries between the groups. We define a barycentre for every probability measure on the boundary without atom, extending the Douady-Earle construction.