  We prove an isoperimetric inequality for probability measures $\mu$ on
$\mathbb{R}^n$ with density proportional to $\exp(-\phi(\lambda | x|))$, where
$|x|$ is the euclidean norm on $\mathbb{R}^n$ and $\phi$ is a non-decreasing
convex function. It applies in particular when $\phi(x)=x^\alpha$ with
$\alpha\ge1$. Under mild assumptions on $\phi$, the inequality is
dimension-free if $\lambda$ is chosen such that the covariance of $\mu$ is the
identity.
