Observable concentration of mm-spaces into spaces with doubling measures

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6 Citations (Scopus)

Abstract

The property of measure concentration is that an arbitrary 1-Lipschitz function f : X → 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.

Original languageEnglish
Pages (from-to)49-56
Number of pages8
JournalGeometriae Dedicata
Volume127
Issue number1
DOIs
Publication statusPublished - 2007 Jun

Keywords

  • Doubling measure
  • Observable diameter
  • Separation distance
  • mm-space

ASJC Scopus subject areas

  • Geometry and Topology

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