Metric Spaces where Geodesics are Never Unique
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913821110566912 |
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| author | Banaji, Amlan |
| author_facet | Banaji, Amlan |
| contents | This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed spaces and deduce that $(C([0,1]),||\cdot||_1)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00598 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Metric Spaces where Geodesics are Never Unique Banaji, Amlan Metric Geometry Classical Analysis and ODEs 51F99 (Primary), 46B20, 52A21 (Secondary) This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed spaces and deduce that $(C([0,1]),||\cdot||_1)$ 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. |
| title | Metric Spaces where Geodesics are Never Unique |
| topic | Metric Geometry Classical Analysis and ODEs 51F99 (Primary), 46B20, 52A21 (Secondary) |
| url | https://arxiv.org/abs/2209.00598 |