This is an announcement for the paper "Centroid bodies and the logarithmic Laplace transform - A unified approach" by Boaz Klartag and Emanuel Milman.

Abstract: We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi-2 constant is obtained. Along the way, we present some new bounds on the volume of L_p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the L_p-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author.

Archive classification: math.FA

Submitted from: klartagb@post.tau.ac.il

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

http://front.math.ucdavis.edu/1103.2985

or

http://arXiv.org/abs/1103.2985