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arXiv · 1408.5793

A metric characterization of snowflakes of Euclidean spaces

Kyle Kinneberg·Enrico Le Donne
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Abstract

We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\mathbb R^n$ equipped with a distance $(d_{\rm E})^\epsilon$, for some $n\in \mathbb N_0$ and $\epsilon\in (0,1]$, where $d_{\rm E}$ is the Euclidean distance, if and only if it is locally compact, $2$-point isometrically homogeneous, and admits dilations of any factor.

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Kyle Kinneberg, Enrico Le Donne. 2014-08-25. A metric characterization of snowflakes of Euclidean spaces. https://arxiv.org/abs/1408.5793

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