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.

Isometric embeddings of snowflakes into finite-dimensional Banach spaces

Le Donne, Enrico;
2017-01-01

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.
2017
Le Donne, Enrico; Rajala, Tapio; Walsberg, Erik
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/976287
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