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Approximate Gaussian Isoperimetry for k Sets

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

Abstract

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.

Keywords

Gaussian Measure Gaussian Isoperimetric Inequality Voronoi Cell Standard Gaussian Vector Main Technical Tool 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Supported by the Israel Science Foundation.

References

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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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