Calculus of Variations and Geometric Measure Theory

M. Barchiesi - A. Brancolini - V. Julin

Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

created by barchiesi on 07 Sep 2014
modified by paolini on 29 Jan 2018


Published Paper

Inserted: 7 sep 2014
Last Updated: 29 jan 2018

Journal: Ann. Probab.
Volume: 45
Number: 2
Pages: 668--697
Year: 2017
Doi: 10.1214/15-AOP1072

In the "improved version" the constant $c$ in the Main Theorem is calculated in a better way.

Links: official version


We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.

Keywords: quantitative isoperimetric inequality