This is an announcement for the paper "Stability of the reverse Blaschke-Santalo inequality for unconditional convex bodies" by Jaegil Kim and Artem Zvavitch.

Abstract: Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in R^n. The corresponding inequality to the conjecture is sometimes called the the reverse Blaschke-Santalo inequality. The conjecture is known in dimension two and in several special cases. In the class of unconditional convex bodies, Saint Raymond confirmed the conjecture, and Meyer and Reisner, independently, characterized the equality case. In this paper we present a stability version of these results and also show that any symmetric convex body, which is sufficiently close to an unconditional body, satisfies the the reverse Blaschke-Santalo inequality.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A20, 53A15, 52B10

Submitted from: jkim@math.kent.edu

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

http://front.math.ucdavis.edu/1302.5719

or

http://arXiv.org/abs/1302.5719