The Brunn-Minkowski inequality for the generalized Gaussian distribution

Ge Xiong, Kai-Wen Yang

Let $\hat{I}{¼}_p$ be the generalized Gaussian distribution on ${\mathbb{R}}^n$ with density $e^{-\frac{|x{|}^p}{p}}$ multiplied by a constant depending on $p\ge 1$ and $n$, and $\hat{I}{\pm }_p(n)$ be t…