Metric spaces where geodesics are never unique

Amlan Banaji

doi:10.1080/00029890.2023.2231332

Metric spaces where geodesics are never unique

Amlan Banaji^*

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	747-754
Number of pages	8
Journal	The American Mathematical Monthly
Volume	130
Issue number	8
Early online date	24 Jul 2023
DOIs	https://doi.org/10.1080/00029890.2023.2231332
Publication status	Published - 1 Aug 2023

Keywords

Geodesics
Multigeodesic spaces

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10.1080/00029890.2023.2231332

Banaji_2023_AMM_Metric-spaces_AAM
Copyright © 2023 The Mathematical Association of America. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1080/00029890.2023.2231332.
Accepted author manuscript, 503 KB

https://arxiv.org/abs/2209.00598Licence: Other

New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
The Leverhulme Trust
1/09/19 → 31/01/23
Project: Standard

Cite this

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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.",

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Metric spaces where geodesics are never unique

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Keywords

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New perspectives in the dimension: New perspectives in the dimension theory of fractals

Cite this