Approximate Gaussian Isoperimetry for k Sets

  • Gideon SchechtmanEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)


Given 2 ≤ kn, 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.


Gaussian Measure Gaussian Isoperimetric Inequality Voronoi Cell Standard Gaussian Vector Main Technical Tool 
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Supported by the Israel Science Foundation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael

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