Calculus of Variations and Geometric Measure Theory
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E. Le Donne - T. Rajala - E. Walsberg

Isometric embeddings of snowflakes into finite-dimensional Banach spaces

created by ledonne on 21 Dec 2018

[BibTeX]

preprint

Inserted: 21 dec 2018

Year: 2016

ArXiv: 1609.03377 PDF

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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