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arXiv · 1110.5551

Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

S. Artstein-Avidan·B. Klartag·C. Schuett·E. Werner
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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.

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S. Artstein-Avidan, B. Klartag, C. Schuett, E. Werner. 2011-10-25. Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality. https://arxiv.org/abs/1110.5551

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