An isoperimetric inequality on the $\ell_p$ balls

Details An isoperimetric inequality on the $\ell_p$ balls An isoperimetric inequality on the $\ell_p$ balls

2006-07-17

arxiv.org/abs/math/0607398v3

Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques 2008, Vol. 44, No. 2, 362-373

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AIHP121 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiqu

Scientific paper

10.1214/07-AIHP121

The normalised volume measure on the $\ell_p^n$ unit ball ($1\leq p\leq 2$)
satisfies the following isoperimetric inequality: the boundary measure of a set
of measure $a$ is at least $cn^{1/p}\tilde{a}\log^{1-1/p}(1/\tilde{a})$, where
$\tilde{a}=\min(a,1-a)$.

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