Calculus of Variations and Geometric Measure Theory
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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 27 Aug 2021


Submitted Paper

Inserted: 20 nov 2020
Last Updated: 27 aug 2021

Pages: 20
Year: 2020


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


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