Isometric embeddings of snowflakes into finitedimensional Banach spaces
Le Donne, E., Rajala, T., & Walsberg, E. (2018). Isometric embeddings of snowflakes into finitedimensional Banach spaces. Proceedings of the American Mathematical Society, 146(2), 685693. https://doi.org/10.1090/proc/13778
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Proceedings of the American Mathematical SocietyDate
2018Copyright
© 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 finitedimensional 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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American Mathematical SocietyISSN Search the Publication Forum
00029939Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/27796618
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Academy of FinlandFunding program(s)
Research post as Academy Research Fellow, AoFAdditional information about funding
The 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 (FP7/20072013) / ERC Grant agreement no. 291111/ MODAGLicense
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