Isometric embeddings of snowflakes into finite-dimensional Banach spaces
Le Donne, E., Rajala, T., & Walsberg, E. (2018). Isometric embeddings of snowflakes into finite-dimensional Banach spaces. Proceedings of the American Mathematical Society, 146(2), 685-693. https://doi.org/10.1090/proc/13778
Published inProceedings of the American Mathematical Society
© 2017 American Mathematical Society
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.
PublisherAmerican Mathematical Society
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
Additional information about fundingThe first and second authors acknowledge the support of the Academy of Finland, projects no. 288501 and 274372 The third author acknowledges the support of the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 291111/ MODAG
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