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Conformal Geometry and Dynamics

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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
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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Additional Information

Gabriel Pallier
Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
Email: gabriel.pallier@math.u-psud.fr, gabriel.pallier@dm.unipi.it

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