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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15159 |
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| _version_ | 1866918294072590336 |
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| author | Bate, David Valentine, Phoebe |
| author_facet | Bate, David Valentine, Phoebe |
| contents | We prove that in a complete metric space $X$, $1$-rectifiability of a set $E\subset X$ with $\mathcal{H}^1(E)<\infty$ and positive lower density $\mathcal{H}^1$-a.e. is implied by the property that all tangent spaces are connected metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterising 1-rectifiable metric spaces via connected tangent spaces Bate, David Valentine, Phoebe Metric Geometry We prove that in a complete metric space $X$, $1$-rectifiability of a set $E\subset X$ with $\mathcal{H}^1(E)<\infty$ and positive lower density $\mathcal{H}^1$-a.e. is implied by the property that all tangent spaces are connected metric spaces. |
| title | Characterising 1-rectifiable metric spaces via connected tangent spaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2503.15159 |