Sublinear quasiconformality and the large-scale geometry of Heintze groups

Gabriel Pallier (1)

1 UP11 - Université Paris-Sud - Paris 11

This article analyzes sublinearly quasisymmetric homeo-morphisms (generalized quasisymmetric mappings), and draws applications to the sublinear large-scale geometry of negatively curved groups and spaces. It is proven that those homeomorphisms lack analytical properties but preserve a conformal dimension and appropriate function spaces, distinguishing certain (nonsymmetric) Riemannian negatively curved homogeneous spaces, and Fuchsian buildings, up to sublinearly biLipschitz equivalence (generalized quasiisometry).

Domaines: Géométrie métrique [math.MG]; Théorie des groupes [math.GR]

Gabriel Pallier. Sublinear quasiconformality and the large-scale geometry of Heintze groups. Conformal Geometry and Dynamics of the American Mathematical Society, 2020, 24 (7), pp.131-163. ⟨10.1090/ecgd/352⟩. ⟨hal-02134190v3⟩