More on functional and quantitative versions of the isoperimetric inequality
Functional Analysis
2017-01-04 v3
Abstract
This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein distance of the classical isopemetric inequality. In both parts, we use optimal transportation. Finally, we use our refined isoperimetric inequality in some classical cases arising in convex geometry.
Keywords
Cite
@article{arxiv.1609.04179,
title = {More on functional and quantitative versions of the isoperimetric inequality},
author = {Erik Thomas},
journal= {arXiv preprint arXiv:1609.04179},
year = {2017}
}