## Bernoulli

- Bernoulli
- Volume 23, Number 2 (2017), 1056-1081.

### Perimeters, uniform enlargement and high dimensions

#### Abstract

We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a constant which does not depend on the number of factors. Such dimension free bounds have applications to the study of influences of variables.

#### Article information

**Source**

Bernoulli, Volume 23, Number 2 (2017), 1056-1081.

**Dates**

Received: December 2014

Revised: September 2015

First available in Project Euclid: 4 February 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1486177392

**Digital Object Identifier**

doi:10.3150/15-BEJ769

**Mathematical Reviews number (MathSciNet)**

MR3606759

**Zentralblatt MATH identifier**

1378.60012

**Keywords**

influences isoperimetry

#### Citation

Barthe, Franck; Huou, Benoît. Perimeters, uniform enlargement and high dimensions. Bernoulli 23 (2017), no. 2, 1056--1081. doi:10.3150/15-BEJ769. https://projecteuclid.org/euclid.bj/1486177392