Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Cito - D. A. La Manna - D. Pallara

A quantitative dimension free isoperimetric inequality for the Fractional Gaussian Perimeter

created by carbotti on 20 Nov 2020
modified on 22 Feb 2022


Accepted Paper

Inserted: 20 nov 2020
Last Updated: 22 feb 2022

Journal: Communications in Analysis and Geometry
Pages: 20
Year: 2022

ArXiv: 2011.10451 PDF


We prove a quantitative isoperimetric inequality for the Gaussian fractional perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing in the inequality does not depend on the dimension but only on the Gaussian volume of the set and on the fractional parameter.

Keywords: Isoperimetric inequalities, stability inequalities, Fractional perimeters, Fractional Ornstein-Uhlenbeck, Extension Techniques