This is an announcement for the paper "Some functional forms of Blaschke-Santal'o inequality" by Matthieu Fradelizi and Mathieu Meyer.

Abstract: We establish new functional versions of the Blaschke-Santal'o inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of K.~Ball and we give a simple proof of the case of equality. As a corollary, we get some inequalities for $\log$-concave functions and Legendre transforms which extend the recent result of Artstein, Klartag and Milman, with its equality case.

Archive classification: Functional Analysis; Metric Geometry

Mathematics Subject Classification: 52A40

Remarks: 19 pages, to appear in Mathematische Zeitschrift

The source file(s), Blaschke-Santalo-final.tex: 48038 bytes, is(are) stored in gzipped form as 0609553.gz with size 15kb. The corresponding postcript file has gzipped size 71kb.

Submitted from: matthieu.fradelizi@univ-mlv.fr

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

http://front.math.ucdavis.edu/math.FA/0609553

or

http://arXiv.org/abs/math.FA/0609553

or by email in unzipped form by transmitting an empty message with subject line

uget 0609553

or in gzipped form by using subject line

get 0609553

to: math@arXiv.org.