A metric characterization of snowflakes of Euclidean spaces

2014/08/25 by Kinneberg, Kyle, Donne, Enrico Le
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1408.5793

Abstract

We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to \mathbb Rⁿ equipped with a distance (d_{\rm E})^ε, for some n∈ \mathbb N₀ and ε∈ (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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