This is an announcement for the paper "John's ellipsoid and the integral ratio of a log-concave function" by David Alonso-Gutierrez, Bernardo Gonzalez Merino, Carlos Hugo Jimenez, and Rafael Villa.

Abstract: We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional a?ne isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.

Archive classification: math.FA

Submitted from: bg.merino@tum.de

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

http://front.math.ucdavis.edu/1511.01266

or

http://arXiv.org/abs/1511.01266