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Conformal Geometry and Dynamics

ISSN 1088-4173



Sublinear quasiconformality and the large-scale geometry of Heintze groups

Author: Gabriel Pallier
Journal: Conform. Geom. Dyn. 24 (2020), 131-163
MSC (2010): Primary 20F67, 30L10; Secondary 20F69, 53C23, 53C30, 22E25.
Published electronically: June 19, 2020
MathSciNet review: 4127909
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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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Additional Information

Gabriel Pallier
Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
MR Author ID: 1181101
ORCID: 0000-0002-6219-7262

Received by editor(s): May 20, 2019
Received by editor(s) in revised form: September 14, 2019, and January 15, 2020
Published electronically: June 19, 2020
Additional Notes: The author was supported by ANR-15-CE40-0018SRGI and by ERC Starting Grant 713998 GeoMeG
Article copyright: © Copyright 2020 American Mathematical Society