Functional Versions of Lp-Affine Surface Area and Entropy Inequalities

By Umut Caglar, Matthieu Fradelizi, Olivier Gu'edon, Joseph Lehec, Carsten Schütt, Elisabeth M. Werner. 2014

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In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowskitheory is a modern analogue of the classical Brunn Minkowski theory. A cornerstoneof this theory is the Lp-affine surface area for convex bodies. Here, we introducea functional form of this concept, for log concave and s-concave functions. Weshow that the new functional form is a generalization of the original Lp-affinesurface area. We prove duality relations and affine isoperimetric inequalities for logconcave and s-concave functions. This leads to a new inverse log-Sobolevinequality for s-concave densities

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/e362c53fd1de37bf18bd9801433ecdb2f184e407