  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).
