Sublinear quasiconformality and the large-scale geometry of Heintze groups

Abstract

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).Comment: v1->v2: shortened, revised. Lemma 2.3 and definition of Cdim corrected. Proof of main theorem simplified. Figure 4 adde