Géométrie asymptotique sous-linéaire : hyperbolicité, autosimilarité, invariants

Abstract : Sublinearly biLipschitz equivalences have been introduced by Yves Cornulier as a means of describing the asymptotic cones of Lie groups; they include and generalize quasiisometries. This thesis provides invariants for sublinearly biLipschitz equivalence between Gromov-hyperbolic groups and spaces using analysis on the Gromov boundary. A class of applications generalizing quasisymmetric mappings, and a corresponding conformal dimension, are introduced as tools. Riemannian symmetric spaces of noncompact type as well as a subclass of homogeneous negatively curved Riemannian manifolds are classified up to sublinearly biLipschitz equivalence.
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Gabriel Pallier. Géométrie asymptotique sous-linéaire : hyperbolicité, autosimilarité, invariants. Géométrie métrique [math.MG]. Université Paris-Saclay, 2019. Français. ⟨NNT : 2019SACLS210⟩. ⟨tel-02307649⟩

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