Central and L p -concentration of 1-Lipschitz maps into R-trees

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April, 2009 Central and

L^{p}

-concentration of 1-Lipschitz maps into

\mbi{R}

-trees

Kei FUNANO

J. Math. Soc. Japan 61(2): 483-506 (April, 2009). DOI: 10.2969/jmsj/06120483

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Abstract

In this paper, we study the Lévy-Milman concentration phenomenon of 1-Lipschitz maps from mm-spaces to $\mbi{R}$ -trees. Our main theorems assert that the concentration to $\mbi{R}$ -trees is equivalent to the concentration to the real line.

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Kei FUNANO. "Central and $L^{p}$ -concentration of 1-Lipschitz maps into $\mbi{R}$ -trees." J. Math. Soc. Japan 61 (2) 483 - 506, April, 2009. https://doi.org/10.2969/jmsj/06120483

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Published: April, 2009

First available in Project Euclid: 13 May 2009

zbMATH: 1198.46021

MathSciNet: MR2532898

Digital Object Identifier: 10.2969/jmsj/06120483

Subjects:

Primary: 53C23

Keywords: $\mbi{R}$-tree , median , mm-space , observable $L^{p}$-variation , observable central radius , observable diameter

Rights: Copyright © 2009 Mathematical Society of Japan

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J. Math. Soc. Japan

Vol.61 • No. 2 • April, 2009

Mathematical Society of Japan

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Kei FUNANO "Central and

L^{p}

-concentration of 1-Lipschitz maps into

\mbi{R}

-trees," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 61(2), 483-506, (April, 2009)

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