Metric spaces where geodesics are never unique
Abstract
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimizing geodesics. We provide a simple characterization of multigeodesic normed spaces and deduce that (C([0,1]),||⋅||1) is an example of such a space, but that finite-dimensional normed spaces are not. We also investigate what additional features are possible in arbitrary metric spaces which are multigeodesic.
Citation
Banaji , A 2023 , ' Metric spaces where geodesics are never unique ' , The American Mathematical Monthly , vol. 130 , no. 8 , pp. 747-754 . https://doi.org/10.1080/00029890.2023.2231332
Publication
The American Mathematical Monthly
Status
Peer reviewed
ISSN
0002-9890Type
Journal article
Description
Funding: This work was supported by the Leverhulme Trust under grant RPG-2019-034.Collections
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