Stability of some versions of the Pr\'ekopa-Leindler inequality.

link: http://arxiv.org/abs/0909.3742
Abstract

Two consequences of the stability version of the one dimensional
Pr\'ekopa-Leindler inequality are presented. One is the stability version of
the Blaschke-Santal\'o inequality, and the other is a stability version of the
Pr\'ekopa-Leindler inequality for even functions in higher dimensions, where a
recent stability version of the Brunn-Minkowski inequality is also used in an
essential way.