Perimeters, uniform enlargement and high dimensions
  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. 
Franck Barthe and Benoit Huou
math.FA math.MG math.PR