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Median and injective metric spaces
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Bowditch, B. H. (2020) Median and injective metric spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 168 . pp. 43-55. doi:10.1017/S0305004118000555 ISSN 0305-0041.
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Official URL: https://doi.org/10.1017/S0305004118000555
Abstract
We describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Metric spaces, Geometry | ||||||||
Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society | ||||||||
Publisher: | Cambridge University Press | ||||||||
ISSN: | 0305-0041 | ||||||||
Official Date: | January 2020 | ||||||||
Dates: |
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Volume: | 168 | ||||||||
Page Range: | pp. 43-55 | ||||||||
DOI: | 10.1017/S0305004118000555 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Mathematical Proceedings of the Cambridge Philosophical Society http://doi.org/10.1017/S0305004118000555. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | © Cambridge Philosophical Society 2018 | ||||||||
Date of first compliant deposit: | 20 June 2018 | ||||||||
Date of first compliant Open Access: | 4 February 2019 | ||||||||
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