Observable concentration of mm-spaces into spaces with doubling measures

Kei Funano

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arXiv · math/0701534

Observable concentration of mm-spaces into spaces with doubling measures

Kei Funano

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Abstract

The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any 1-Lipschitz map $f$ from $X$ to a space $Y$ with a doubling measure also concentrates to a constant map. As a corollary, we get any 1-Lipschitz map to a Riemannian manifold with a lower Ricci curvature bounds also concentrates to a constant map.

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BibTeX RIS

Kei Funano. 2007-01-19. Observable concentration of mm-spaces into spaces with doubling measures. https://arxiv.org/abs/math/0701534

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