This is an announcement for the paper "Rogers-Shephard inequality for log-concave functions" by David Alonso-Gutierrez, Bernardo Gonzalez, C. Hugo Jimenez, and Rafael Villa.

Abstract: In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets.

Archive classification: math.FA math.MG

Mathematics Subject Classification: Primary 52A20, Secondary 39B62, 46N10

Remarks: 24 pages

Submitted from: carloshugo@us.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.2556

or

http://arXiv.org/abs/1410.2556