Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917049478938624 |
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| author | Bate, David Wald, Pietro |
| author_facet | Bate, David Wald, Pietro |
| contents | We construct a family of purely PI unrectifiable Lipschitz differentiability spaces and investigate the possible of Banach spaces targets for which Lipschitz differentiability holds. We provide a general investigation into the geometry of \emph{shortcut} metric spaces and characterise when such spaces are PI rectifiable, and when they are $Y$-LDS, for a given $Y$. The family of spaces arises as an example of our characterisations. Indeed, we show that Laakso spaces satisfy the required hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions Bate, David Wald, Pietro Functional Analysis Metric Geometry We construct a family of purely PI unrectifiable Lipschitz differentiability spaces and investigate the possible of Banach spaces targets for which Lipschitz differentiability holds. We provide a general investigation into the geometry of \emph{shortcut} metric spaces and characterise when such spaces are PI rectifiable, and when they are $Y$-LDS, for a given $Y$. The family of spaces arises as an example of our characterisations. Indeed, we show that Laakso spaces satisfy the required hypotheses. |
| title | Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2510.25715 |