  Given $2\le k\le n$, the minimal $(n-1)$-dimensional Gaussian measure of the
union of the boundaries of $k$ disjoint sets of equal Gaussian measure in
$\R^n$ whose union is $\R^n$ is of order $\sqrt{\log k}$. A similar results
holds also for partitions of the sphere $S^{n-1}$ into $k$ sets of equal Haar
measure.
