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arXiv · 2510.03196

A characterization of snowflakes via rectifiability

Emanuele Caputo·Nicola Cavallucci
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Abstract

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.

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Emanuele Caputo, Nicola Cavallucci. 2025-10-03. A characterization of snowflakes via rectifiability. https://arxiv.org/abs/2510.03196

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