English

Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

Functional Analysis 2011-10-26 v1

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.

Keywords

Cite

@article{arxiv.1110.5551,
  title  = {Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality},
  author = {S. Artstein-Avidan and B. Klartag and C. Schuett and E. Werner},
  journal= {arXiv preprint arXiv:1110.5551},
  year   = {2011}
}