This is an announcement for the paper "Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality" by S. Artstein-Avidan, B. Klartag, C. Schuett and E. Werner.

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 inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincar'e inequality for the Gaussian measure.

Archive classification: math.FA

Mathematics Subject Classification: 52A20

Submitted from: elisabeth.werner@case.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1110.5551

or

http://arXiv.org/abs/1110.5551