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arXiv · 2209.00598

Metric Spaces where Geodesics are Never Unique

Amlan Banaji
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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 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.

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Amlan Banaji. 2022-09-01. Metric Spaces where Geodesics are Never Unique. https://doi.org/10.1080/00029890.2023.2231332

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