Toward a quasi-Möbius characterization of invertible homogeneous metric spaces
Year of publication
2021
Authors
Freeman, David; Le Donne, Enrico
Abstract
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.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Volume
37
Issue
2
Pages
671-722
ISSN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
No
Self-archived
No
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object]
Publication country
Switzerland
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.4171/rmi/1211
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes