An isoperimetric inequality on the ℓp balls

Sasha Sodin

doi:10.1214/07-AIHP121

An isoperimetric inequality on the ℓ_p balls

Sasha Sodin^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The normalised volume measure on the ℓ_pⁿ unit ball (1 ≤ p ≤ 2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn^1/pa log ^1-1/p(1/a) , where a = min(a, 1 -a) .

Original language	English
Pages (from-to)	362-373
Number of pages	12
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Issue number	2
DOIs	https://doi.org/10.1214/07-AIHP121
State	Published - Apr 2008

Keywords

Isoperimetric inequalities
Volume measure

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10.1214/07-AIHP121

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abstract = "The normalised volume measure on the ℓpn unit ball (1 ≤ p ≤ 2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pa log 1-1/p(1/a) , where a = min(a, 1 -a) .",

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AB - The normalised volume measure on the ℓpn unit ball (1 ≤ p ≤ 2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pa log 1-1/p(1/a) , where a = min(a, 1 -a) .

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An isoperimetric inequality on the ℓ_p balls

Abstract

Keywords

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