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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.
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Organizations and authors

University of Jyväskylä

Le Donne Enrico Orcid -palvelun logo

Publication type

Publication format

Article

Parent publication type

Journal

Article type

Original article

Audience

Scientific

Peer-reviewed

Peer-Reviewed

MINEDU's publication type classification code

A1 Journal article (refereed), original research

Publication channel information

Volume

37

Issue

2

Pages

671-722

​Publication forum

66402

​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