On Gaussian Brunn–Minkowski inequalities
Volume 191 / 2009
Studia Mathematica 191 (2009), 283-304
MSC: 60E15, 60G15, 52A40, 35K05.
DOI: 10.4064/sm191-3-9
Abstract
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.
