2 problems

Let $G$ be a Carnot group, let $K$ be a non-smooth homogeneous norm on $G$, and consider probability measures with density $e^{-U}$ with respect to Haar measure, where $U=U(K)$. Su…

Let $G$ be a Carnot group and let $N$ be a smooth homogeneous norm on $G$. For a function $U=U(N)$, write $\mu_U$ for the corresponding probability measure with density $e^{-U}$ wi…