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).

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

References in corpus (4)

• Metric Lie groups admitting dilations
• On the quasisymmetric Hölder-equivalence problem for Carnot groups
• On sublinear bilipschitz equivalence of groups
• Relative $L^p$-cohomology and Heintze groups

Cited by in corpus (2)

• Pinched Curvature in Heintze Groups of Carnot-type
• On the logarithmic coarse structures of Lie groups and hyperbolic spaces