A functional form of the isoperimetric inequality for the Gaussian measure

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Abstract

Let g be a smooth function on ℝn with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that φ(Φ-1(Eg)) - Eφ(Φ-1(g)) ≤ E \∇g\. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.

Original languageEnglish (US)
Pages (from-to)39-49
Number of pages11
JournalJournal of Functional Analysis
Volume135
Issue number1
DOIs
StatePublished - Jan 10 1996

Bibliographical note

Funding Information:
* Partially supported by the National Science Foundation and the Air Force Office of Scientific Research Grant 91-0030, the Army Research Office Grant DAAL03-92-G-0008, Grant 93-011-1454 of Russian Foundation for Scientific Research and Grant NXZ000 from the International Science Foundation.

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