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arXiv · 1102.4102

Approximate Gaussian isoperimetry for k sets

Gideon Schechtman
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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.

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Gideon Schechtman. 2011-02-20. Approximate Gaussian isoperimetry for k sets. https://arxiv.org/abs/1102.4102

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