Inserted: 20 nov 2020
Last Updated: 27 aug 2021
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