Approximate Gaussian isoperimetry for k sets

2011/02/20 by Schechtman, Gideon · 1 citation
#52A40 #60E15 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1102.4102

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 \Rⁿ whose union is \Rⁿ is of order √(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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