John's ellipsoid and the integral ratio of a log-concave function
Functional Analysis
2016-10-23 v1
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 affine 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.
Keywords
Cite
@article{arxiv.1511.01266,
title = {John's ellipsoid and the integral ratio of a log-concave function},
author = {David Alonso-Gutiérrez and Bernardo González Merino and Carlos Hugo Jiménez and Rafael Villa},
journal= {arXiv preprint arXiv:1511.01266},
year = {2016}
}