Isoperimetric inequality for radial probability measures on Euclidean spaces

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the Poincaré limit which asserts that the n-dimensional Gaussian measure is approximated by the projections of the uniform probability measure on the Euclidean sphere of appropriate radius to the first n-coordinates as the dimension diverges to infinity. The generalization is done by replacing the projections with certain maps. Using this generalization, we derive a Gaussian isoperimetric inequality for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.

Original languageEnglish
Pages (from-to)3435-3454
Number of pages20
JournalJournal of Functional Analysis
Volume266
Issue number6
DOIs
Publication statusPublished - 2014 Mar 15
Externally publishedYes

Keywords

  • Isoperimetric inequality
  • Poincaré limit

ASJC Scopus subject areas

  • Analysis

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