Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

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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