Sublinear quasiconformality and the large-scale geometry of Heintze groups

Pallier, Gabriel

doi:10.1090/ecgd/352

Sublinear quasiconformality and the large-scale geometry of Heintze groups
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by Gabriel Pallier

Conform. Geom. Dyn. 24 (2020), 131-163

DOI: https://doi.org/10.1090/ecgd/352

Published electronically: June 19, 2020

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Abstract:

This article analyzes sublinearly quasisymmetric homeomorphisms (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 quasi-isometry).

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