We are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for m Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp-Lieb inequality and of its reverse form, which follow exactly the same lines.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-9,
author = {Franck Barthe and Nolwen Huet},
title = {On Gaussian Brunn-Minkowski inequalities},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {283-304},
zbl = {1166.60014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-9}
}
Franck Barthe; Nolwen Huet. On Gaussian Brunn-Minkowski inequalities. Studia Mathematica, Tome 192 (2009) pp. 283-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-9/