Functional versions of L_p-affine surface area and entropy inequalities
Functional Analysis
2014-02-14 v1
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.
Keywords
Cite
@article{arxiv.1402.3250,
title = {Functional versions of L_p-affine surface area and entropy inequalities},
author = {U. Caglar and M. Fradelizi and O. Guedon and J. Lehec and C. Schuett and E. M. Werner},
journal= {arXiv preprint arXiv:1402.3250},
year = {2014}
}