Sublinear quasiconformality and the large-scale geometry of Heintze groups
Metric Geometry
2020-03-02 v3 Group Theory
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).
Keywords
Cite
@article{arxiv.1905.08981,
title = {Sublinear quasiconformality and the large-scale geometry of Heintze groups},
author = {Gabriel Pallier},
journal= {arXiv preprint arXiv:1905.08981},
year = {2020}
}
Comments
v1->v2: shortened, revised. Lemma 2.3 and definition of Cdim corrected. Proof of main theorem simplified. Figure 4 added