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arXiv · 1609.03377

Isometric embeddings of snowflakes into finite-dimensional Banach spaces

Enrico Le Donne·Tapio Rajala·Erik Walsberg
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Abstract

We consider a general notion of snowflake of a metric space by composing the distance by 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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Enrico Le Donne, Tapio Rajala, Erik Walsberg. 2016-09-12. Isometric embeddings of snowflakes into finite-dimensional Banach spaces. https://arxiv.org/abs/1609.03377

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