  It was shown by K. Ball and F. Nazarov, that the maximal surface area of a
convex set in $\mathbb{R}^n$ with respect to the Standard Gaussian measure is
of order $n^{\frac{1}{4}}$. In the present paper we establish the analogous
result for all rotation invariant log concave probability measures. We show
that the maximal surface area with respect to such measures is of order
$\frac{\sqrt{n}}{\sqrt[4]{Var|X|} \sqrt{\mathbb{E}|X|}}$, where $X$ is a random
vector in $\mathbb{R}^n$ distributed with respect to the measure.
