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arXiv · 2510.25715

Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions

David Bate·Pietro Wald
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Abstract

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.

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David Bate, Pietro Wald. 2025-10-29. Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions. https://arxiv.org/abs/2510.25715

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