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Published in:
2012 | OriginalPaper | Chapter
Approximate Gaussian Isoperimetry for k Sets
Author : Gideon Schechtman
Published in: Geometric Aspects of Functional Analysis
Publisher: Springer Berlin Heidelberg
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Abstract
Given 2 ≤ k ≤ n, the minimal (n − 1)-dimensional Gaussian measure of the union of the boundaries of \(k\) disjoint sets of equal Gaussian measure in \({\mathbb{R}}^{n}\) whose union is \({\mathbb{R}}^{n}\) 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.