The dimensional Brunn-Minkowski inequality in Gauss space

Alexandros Eskenazis, Georgios Moschidis

Let ${\gamma }_n$ be the standard Gaussian measure on ${\mathbb{R}}^n$. We prove that for every symmetric convex sets $K,L$ in ${\mathbb{R}}^n$ and every $\lambda \in (0,1)$, $$γ_n(λK+(1-λ)L)^{\frac{1…