| An isoperimetric inequality on the $\ell_p$ balls (2006) | |||||||||
Abstract | |||||||||
| 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 $\tilde{a}=\min(a,1-a)$.. Comment: Published in at http://dx.doi.org/10.1214/07-AIHP121 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |||||||||
Publication details | |||||||||
| |||||||||