Isometric embeddings of snowflakes into finite-dimensional Banach spaces

Le Donne, Enrico; Rajala, Tapio; Walsberg, Erik

doi:10.1090/proc/13778

Isometric embeddings of snowflakes into finite-dimensional Banach spaces
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by Enrico Le Donne, Tapio Rajala and Erik Walsberg PDF

Proc. Amer. Math. Soc. 146 (2018), 685-693 Request permission

Abstract:

We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.

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