Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

S. Artstein-Avidan, B. Klartag, C. Schütt, E. Werner

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Abstract

We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure.

Original languageEnglish (US)
Pages (from-to)4181-4204
Number of pages24
JournalJournal of Functional Analysis
Volume262
Issue number9
DOIs
StatePublished - May 1 2012

Bibliographical note

Funding Information:
* Corresponding author at: Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA. E-mail addresses: shiri@post.tau.ac.il (S. Artstein-Avidan), klartagb@tau.ac.il (B. Klartag), schuett@math.uni-kiel.de (C. Schütt), elisabeth.werner@case.edu (E. Werner). 1 Partially supported by BSF grant No. 2006079 and by ISF grant No. 865/07. 2 Partially supported by an ISF grant and an IRG grant. 3 Partially supported by NSF grant and BSF grant No. 2006079.

Keywords

  • Affine isoperimetric inequality
  • Logarithmic Sobolev inequality

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