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## Approximate Gaussian isoperimetry for k sets

### 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

Topics: Mathematics - Probability, Mathematics - Functional Analysis, 60E15, 52A40
Year: 2011
OAI identifier: oai:arXiv.org:1102.4102