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 Gaussian Fractional Perimeter

created by carbotti on 20 Nov 2020
modified on 30 Dec 2020

[BibTeX]

Submitted Paper

Inserted: 20 nov 2020
Last Updated: 30 dec 2020

Pages: 19
Year: 2020

Abstract:

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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