Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

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

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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
Issue number9
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: (S. Artstein-Avidan), (B. Klartag), (C. Schütt), (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.


  • 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