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Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality |
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| Authors: | S. Artstein-Avidan B. Klartag C. Schütt E. Werner |
| Affiliation: | 1. School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel;2. Mathematisches Institut, Universität Kiel, 24105 Kiel, Germany;3. Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA;4. Université de Lille 1, UFR de Mathématique, 59655 Villeneuve d?Ascq, France |
| 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. |
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