Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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


  • Affine isoperimetric inequality
  • Logarithmic Sobolev inequality


Dive into the research topics of 'Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality'. Together they form a unique fingerprint.

Cite this