On Gaussian Brunn-Minkowski inequalities
In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also allows us to have semigroup proofs of the geometric Brascamp-Lieb inequality and of the reverse one which follow exactly the same lines.