Approximate Gaussian Isoperimetry for k Sets

DOI10.1007/978-3-642-29849-3_23zbMATH Open1264.60011arXiv1102.4102OpenAlexW1615581913MaRDI QIDQ4913030

Gideon Schechtman

Publication date: 3 April 2013

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Abstract: Given $2leklen$, 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 $sqrtlogk$. A similar results holds also for partitions of the sphere $S^{n-1}$ into $k$ sets of equal Haar measure.

Full work available at URL: https://arxiv.org/abs/1102.4102

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Geometric probability and stochastic geometry (60D05) Length, area, volume, other geometric measure theory (28A75)

Related Items (3)

Mean isoperimetry with control on outliers: exact and approximation algorithms ⋮ The Gaussian double-bubble and multi-bubble conjectures ⋮ Robust dimension free isoperimetry in Gaussian space

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