This is an announcement for the paper "Approximate Gaussian isoperimetry for k sets" by Gideon Schechtman.

Abstract: 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.

Archive classification: math.PR math.FA

Mathematics Subject Classification: 60E15, 52A40

Submitted from: gideon@weizmann.ac.il

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1102.4102

or

http://arXiv.org/abs/1102.4102