Abstract
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 \ge 1
. Under mild assumptions on
\phi
, the inequality is dimension-free if
\lambda
is chosen such that the covariance of
\mu
is the identity.