Calculus of Variations and Geometric Measure Theory

G. Pallier

Sublinear quasiconformality and the large-scale geometry of Heintze groups

created by pallier on 02 Mar 2020
modified on 06 Aug 2020


Published Paper

Inserted: 2 mar 2020
Last Updated: 6 aug 2020

Journal: Conformal Geometry and Dynamics
Volume: 24
Pages: 131-163
Year: 2020

ArXiv: 1905.08981 PDF


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).

Tags: GeoMeG