This is an announcement for the paper "Functional versions of L_p-affine surface area and entropy" by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Schuett and E. M. Werner.
Abstract: In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities.
Archive classification: math.FA
Submitted from: elisabeth.werner@case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.3250
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