A1 Journal article (refereed)
Toward a quasi-Möbius characterization of invertible homogeneous metric spaces (2021)

Freeman, D., & Le Donne, E. (2021). Toward a quasi-Möbius characterization of invertible homogeneous metric spaces. Revista Matematica Iberoamericana, 37(2), 671-722. https://doi.org/10.4171/rmi/1211

JYU authors or editors

Publication details

All authors or editors: Freeman, David; Le Donne, Enrico

Journal or series: Revista Matematica Iberoamericana

ISSN: 0213-2230

eISSN: 2235-0616

Publication year: 2021

Volume: 37

Issue number: 2

Pages range: 671-722

Publisher: European Mathematical Society Publishing House

Publication country: Switzerland

Publication language: English

DOI: https://doi.org/10.4171/rmi/1211

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1812.03313


We study locally compact metric spaces that enjoy various forms of homogeneity with respect to Möbius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particular, we provide a new characterization of snowflakes of boundaries of rank-one symmetric spaces of non-compact type among locally compact and connected metric spaces. Furthermore, we investigate the metric implications of homogeneity with respect to uniformly strongly quasi-Möbius self-homeomorphisms, connecting such homogeneity with the combination of uniform bi-Lipschitz homogeneity and quasi-invertibility. In this context we characterize spaces containing a cut point and provide several metric properties of spaces containing no cut points. These results are motivated by a desire to characterize the snowflakes of boundaries of rank-one symmetric spaces up to bi-Lipschitz equivalence.

Keywords: complex analysis; metric spaces

Free keywords: Möbius maps; isometric homogeneity; bi-Lipschitz homogeneity; Ptolemy space; quasiinversion; rank-one symmetric space; metric Lie group; Heisenberg group

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 2

Last updated on 2021-07-07 at 17:55