We prove an isoperimetric inequality for probability measures p, on R(n) with density proportional to exp(-phi(lambda vertical bar x vertical bar)), where vertical bar x vertical bar is the euclidean norm on R(n) and phi is a non-decreasing convex function. It applies in particular when phi(x) = x(alpha) with alpha >= 1. Under mild assumptions on phi, the inequality is dimension-free if is chosen such that the covariance of mu is the identity.
展开▼
