A quantitative dimension free isoperimetric inequality for the fractional Gaussian perimeter

2020/11/20 by Alessandro Carbotti, Carbotti, Alessandro, Simone Cito +5 · 2 citations
Mathematics · #35R11 #49Q20 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Numerical methods in inverse problems #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2011.10451

openalex publication_date 2020/11/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

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• The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities
• Optimality and stability of the radial shapes for the Sobolev trace constant

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