  We show that the conjecture of Kannan, Lov\'{a}sz, and Simonovits on
isoperimetric properties of convex bodies and log-concave measures, is true for
log-concave measures of the form $\rho(|x|_B)dx$ on $\mathbb{R}^n$ and
$\rho(t,|x|_B) dx$ on $\mathbb{R}^{1+n}$, where $|x|_B$ is the norm associated
to any convex body $B$ already satisfying the conjecture. In particular, the
conjecture holds for convex bodies of revolution.
