A characterization of snowflakes via rectifiability
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908574676942848 |
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| author | Caputo, Emanuele Cavallucci, Nicola |
| author_facet | Caputo, Emanuele Cavallucci, Nicola |
| contents | We prove a generalization of Tyson-Wu's characterization of metric spaces biLipschitz equivalent to snowflakes to every metric space, by removing compactness, doubling and embeddability assumptions. We also characterize metric spaces that are biLipschitz equivalent to a snowflake in terms of the absence of non-trivial metric $1$-currents in every ultralimit, or equivalently in terms of purely $1$-unrectifiability of every ultralimit. Finally, we discuss some applications and examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of snowflakes via rectifiability Caputo, Emanuele Cavallucci, Nicola Metric Geometry Classical Analysis and ODEs 54E35, 28A80 We prove a generalization of Tyson-Wu's characterization of metric spaces biLipschitz equivalent to snowflakes to every metric space, by removing compactness, doubling and embeddability assumptions. We also characterize metric spaces that are biLipschitz equivalent to a snowflake in terms of the absence of non-trivial metric $1$-currents in every ultralimit, or equivalently in terms of purely $1$-unrectifiability of every ultralimit. Finally, we discuss some applications and examples. |
| title | A characterization of snowflakes via rectifiability |
| topic | Metric Geometry Classical Analysis and ODEs 54E35, 28A80 |
| url | https://arxiv.org/abs/2510.03196 |